Paper Citation Record · LEDGER

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$

As of 8 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 2 inbound Pith citation observations for arXiv:2606.09555.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.09555 v2

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T12:14:26.168036Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T17:42:05.728556Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-08T06:44:40.187746Z

Reference resolution

47 of 47 outbound references displayed

verified exact0
verified fuzzy0
unresolved47
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 01fcec70-d456-4cfe-b284-8612f3bd7d56 · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.034286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ed4c594-ca5c-4b39-8016-4882001be4c0 · outbound

This paper cites Aubin, Probl` emes isop´ erim´ etriques et espaces de Sobolev,J.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Aubin, Probl` emes isop´ erim´ etriques et espaces de Sobolev,J

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.038179Z

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Observation db371bbe-1980-4848-b04e-7437865d03b7 · outbound

This paper cites Bianchi and H.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Bianchi and H

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.041341Z

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Observation c679cf75-3f3a-49c4-a307-4abf01eea245 · outbound

This paper cites Br´ ezis and E.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Br´ ezis and E

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.044606Z

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Observation ebb6325f-d67b-4bcc-b155-a2476a0c7db5 · outbound

This paper cites Brezis and E.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Brezis and E

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.047845Z

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Observation 6f3a7d4d-975e-4fd1-821e-5303f3701c78 · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.051104Z

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Observation 688370c1-4d9a-4835-ad28-8a3ec2619d0d · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.054444Z

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Observation bf4d9ff1-6ebe-4959-9f33-9961c513a86c · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.057167Z

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Observation 222b2beb-3ee5-4176-a3ba-d33619400b4e · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.059799Z

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Observation 256f34e3-37e5-4776-99e8-d2cbb99e3f3e · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.062511Z

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Observation 4c3e38b6-7568-4a2e-8786-48faa3d85e27 · outbound

This paper cites Cianchi, N.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Cianchi, N

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.065533Z

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Observation b35004d1-b1c1-4a1c-b15d-139005e4e8cf · outbound

This paper cites Cianchi, E.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Cianchi, E

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.068373Z

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Observation f291be5d-785d-4d44-9330-ab8049f65aab · outbound

This paper cites Dai and Y.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Dai and Y

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.071121Z

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Observation 579f1119-b5ad-4fb2-9274-3f5482957739 · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.073944Z

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Observation 637fdb05-8e0a-460a-a085-2d9847d30f00 · outbound

This paper cites Dolbeault, M.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Dolbeault, M

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.076631Z

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Observation 4bc09d3e-3580-4249-aee4-8bde654aa9cf · outbound

This paper cites Erd´ elyi, W.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Erd´ elyi, W

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.079370Z

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Observation b289d752-3273-4537-9505-b28734f50149 · outbound

This paper cites Fan, G.-D.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Fan, G.-D

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.082007Z

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Observation 2bd0b251-dcea-4ca1-a470-c7c86ce7daf5 · outbound

This paper cites Figalli, F.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Figalli, F

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.084853Z

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Observation 25da707d-9b7d-4095-bd8c-ca05c00f536c · outbound

This paper cites Figalli and R.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Figalli and R

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.087445Z

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Observation d14b5b3b-e8f5-46fd-a581-9c29aa163a08 · outbound

This paper cites Figalli and Y.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Figalli and Y

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.090400Z

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Observation 31862080-971e-45ad-96a1-850f5b151df4 · outbound

This paper cites Fusco, F.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Fusco, F

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.093404Z

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Observation 55b47d85-3e31-47a6-bd07-475c28c3c388 · outbound

This paper cites Haberl and F.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Haberl and F

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.096313Z

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Observation a148a716-295c-47ee-9ff8-9554ca347d2e · outbound

This paper cites Haberl, F.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Haberl, F

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.099174Z

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Unavailable: canonical work link unavailable.

Observation 1367e1fe-d5d3-4e0a-898e-482739de96dc · outbound

This paper cites Haddad, C.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Haddad, C

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.102114Z

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Observation d3f69888-3ab4-4e4e-b1f6-ad9e5245d083 · outbound

This paper cites Haddad, C.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Haddad, C

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.104754Z

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Observation 6e0a5eed-43ac-4f1a-963a-faaf821c53c4 · outbound

This paper cites Haddad and M.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Haddad and M

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.107461Z

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Observation 1a2fd351-9764-4cf5-afca-71af59d6a0f9 · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.110092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 365f82f1-d449-4ef6-be6a-9d0ed97dbac2 · outbound

This paper cites Jaffard, Analysis of the lack of compactness in the critical Sobolev embeddings,J.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Jaffard, Analysis of the lack of compactness in the critical Sobolev embeddings,J

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.113220Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25b73de7-061c-47fe-a650-28b4c46b3cfd · outbound

This paper cites K¨ onig, On the sharp constant in the Bianchi-Egnell stability inequality,Bull.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ K¨ onig, On the sharp constant in the Bianchi-Egnell stability inequality,Bull

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.115883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3659d068-5617-44cb-ac09-916af8149da0 · outbound

This paper cites Lions, The concentration-compactness principle in the calculus of variations.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Lions, The concentration-compactness principle in the calculus of variations

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.118677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e3cd7b3-0aa3-49ab-9c96-fdad209a157e · outbound

This paper cites Lions, The concentration-compactness principle in the calculus of variations.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Lions, The concentration-compactness principle in the calculus of variations

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.121234Z

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Unavailable: canonical work link unavailable.

Observation ecbd41a6-03f0-4763-a242-a5e668c1df7b · outbound

This paper cites Lutwak, D.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Lutwak, D

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.124481Z

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Unavailable: canonical work link unavailable.

Observation dfec36bf-6c2b-4a9d-b4e5-615701f377d3 · outbound

This paper cites Lutwak, D.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Lutwak, D

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.127312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5eea1600-5a5a-4835-bd2d-671cdd7f8be1 · outbound

This paper cites Neumayer, A note on strong-form stability for the Sobolev inequality,Calc.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Neumayer, A note on strong-form stability for the Sobolev inequality,Calc

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.130001Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e4dafd8-888b-4d2a-8629-b78e036e982c · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.132797Z

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Unavailable: canonical work link unavailable.

Observation 4420125e-35be-4a96-8881-a08dcabeb06a · outbound

This paper cites an unresolved cited work.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.135568Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a242c7b-5ad6-4898-bf92-eea432046ea4 · outbound

This paper cites Pistoia and G.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Pistoia and G

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.138756Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80814aa8-c62a-4d85-b505-d97e7de749f9 · outbound

This paper cites Schneider,Convex bodies: the Brunn-Minkowski theory, vol.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Schneider,Convex bodies: the Brunn-Minkowski theory, vol

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.141597Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7794e54-96d1-4d79-9b91-5f56bbcb6344 · outbound

This paper cites A Stability Result for a Family of Sharp Gagliardo-Nirenberg Inequalities.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ A Stability Result for a Family of Sharp Gagliardo-Nirenberg Inequalities

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.144430Z

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Unavailable: canonical work link unavailable.

Observation db3827e5-c6d7-45ba-95ca-3b2cb1357707 · outbound

This paper cites Solimini, A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space,Ann.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Solimini, A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space,Ann

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.147927Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7482cf4-7d11-4d4a-9b3e-0b676aef7ca9 · outbound

This paper cites Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities,Math.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities,Math

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.150840Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78d7cec3-affa-4014-bf49-0aae6649f224 · outbound

This paper cites Talenti, Best constant in Sobolev inequality,Ann.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Talenti, Best constant in Sobolev inequality,Ann

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.153704Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8212ffb9-3138-43a1-a15e-84fe428f86ee · outbound

This paper cites Wang, The affine Sobolev-Zhang inequality onBV(R n),Adv.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Wang, The affine Sobolev-Zhang inequality onBV(R n),Adv

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.156575Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3759ddfa-b0ca-41fd-a4c7-4d29942f883f · outbound

This paper cites Wang, The affine P´ olya-Szeg¨ o principle: equality cases and stability,J.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Wang, The affine P´ olya-Szeg¨ o principle: equality cases and stability,J

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.159612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76ef688a-e559-45e8-a1f7-6c8db6252fcb · outbound

This paper cites Zhang and X.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Zhang and X

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.162309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5aae49a-e4d2-4dbd-9ed7-9cb68a8bf298 · outbound

This paper cites Zhang, The affine Sobolev inequality,J.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Zhang, The affine Sobolev inequality,J

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.165043Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7fbdfa8c-ea1f-49bf-904f-bd65e2dcb9dc · outbound

This paper cites Zhang, Y.

Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$ Zhang, Y

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-02T12:14:26.168036Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation bcbcb6ff-f6d2-4cb7-888b-6969cc9108d8 · inbound

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$ cites this paper.

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$ Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-07-08T06:44:40.189630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f970695f-2772-456e-ae32-6b66535346d8 · inbound

Sharp Gradient Stability for the Sobolev Trace Inequality cites this paper.

Sharp Gradient Stability for the Sobolev Trace Inequality Sharp Quantitative Stability for the Affine $p$-Sobolev Inequality, Part I: The Case $2\le p<n$

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.728556Z

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Unavailable: canonical work link unavailable.