Paper Citation Record · LEDGER

Sharp Gradient Stability for the Sobolev Trace Inequality

As of 8 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2607.17588.

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

pith.paper-citation-record.v1
2607.17588 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T17:42:09.293429Z

measured 42 of 42 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T07:34:56.464823Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

41 of 41 outbound references displayed

verified exact6
verified fuzzy0
unresolved30
parse uncertain0
malformed identifier5
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 83d23915-9097-4556-a6e8-da4ae2bc7afe · outbound

This paper cites Agmon, A.

Sharp Gradient Stability for the Sobolev Trace Inequality Agmon, A

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:03.935340Z

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Unavailable: canonical work link unavailable.

Observation 3c5c3285-72fb-401c-a7bd-0afef7cc1727 · outbound

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

Sharp Gradient Stability for the Sobolev Trace Inequality Aubin,Probl` emes isop´ erim´ etriques et espaces de Sobolev, J

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:04.048192Z

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Observation 8009ff90-04bb-4d78-a04e-ce345e9101e5 · outbound

This paper cites Bianchi and H.

Sharp Gradient Stability for the Sobolev Trace Inequality Bianchi and H

Reference 3

Resolution: verified exact; doi, observed 2026-08-01T17:43:23.218637Z

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 56aa7b94-89ff-463d-af94-cb5fe4dba45f · outbound

This paper cites Borthwick,Spectral Theory: Basic Concepts and Applications, Graduate Texts in Mathematics, vol.

Sharp Gradient Stability for the Sobolev Trace Inequality Borthwick,Spectral Theory: Basic Concepts and Applications, Graduate Texts in Mathematics, vol

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:04.304655Z

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Observation fb46ac64-6727-4c25-a6d1-f7b103ebaf05 · outbound

This paper cites Brezis and E.

Sharp Gradient Stability for the Sobolev Trace Inequality Brezis and E

Reference 5

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

Observation 794fc8a4-f594-43e8-b124-5c7a530512ef · outbound

This paper cites Brezis and E.

Sharp Gradient Stability for the Sobolev Trace Inequality Brezis and E

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:04.533888Z

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Observation 877e4765-858e-4fa5-9ae3-7f17feb9db39 · outbound

This paper cites Cianchi, N.

Sharp Gradient Stability for the Sobolev Trace Inequality Cianchi, N

Reference 7

Resolution: verified exact; doi, observed 2026-08-01T17:43:23.081101Z

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 b8a83c59-5c81-4965-890b-6eb531abb527 · outbound

This paper cites Ciraolo, A.

Sharp Gradient Stability for the Sobolev Trace Inequality Ciraolo, A

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:04.785233Z

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Observation d161d2c0-abb9-4a38-bdbf-451931f13f43 · outbound

This paper cites Cordero-Erausquin, B.

Sharp Gradient Stability for the Sobolev Trace Inequality Cordero-Erausquin, B

Reference 9

Resolution: malformed identifier; no resolver link, observed 2026-08-01T17:42:04.894659Z

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Observation 5fb3b578-f0b4-4b2c-a30b-2b286e2ef3a7 · outbound

This paper cites Courant and D.

Sharp Gradient Stability for the Sobolev Trace Inequality Courant and D

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.015275Z

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Observation 832b8dea-9a59-4d6f-ab93-7d05a34b482c · outbound

This paper cites an unresolved cited work.

Sharp Gradient Stability for the Sobolev Trace Inequality Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.214626Z

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Observation 9268cdfd-d5ff-4541-81ad-85da62a34f93 · outbound

This paper cites Dai and Y.

Sharp Gradient Stability for the Sobolev Trace Inequality Dai and Y

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.337952Z

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Observation c1ad684b-2f9f-42da-91d8-ef03d995bd36 · outbound

This paper cites an unresolved cited work.

Sharp Gradient Stability for the Sobolev Trace Inequality Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.471178Z

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Observation e0ed9f03-7724-4bf8-8db3-7c6c90925d63 · outbound

This paper cites an unresolved cited work.

Sharp Gradient Stability for the Sobolev Trace Inequality Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.536916Z

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Observation d8a64454-3863-4432-a56f-135f2fb23f2b · outbound

This paper cites Figalli and F.

Sharp Gradient Stability for the Sobolev Trace Inequality Figalli and F

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.630658Z

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

This paper cites Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2\le p<n\).

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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Observation 6d5986db-795c-46ca-87c0-69f495510dae · outbound

This paper cites Figalli, F.

Sharp Gradient Stability for the Sobolev Trace Inequality Figalli, F

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:05.849770Z

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Observation 05999f35-f2c6-4d1d-82d1-8c234a7d481f · outbound

This paper cites Figalli and R.

Sharp Gradient Stability for the Sobolev Trace Inequality Figalli and R

Reference 18

Resolution: verified exact; doi, observed 2026-08-01T17:43:22.959262Z

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 be7d7603-188f-48fc-9d96-2d31cdf29ac7 · outbound

This paper cites Figalli and Y.

Sharp Gradient Stability for the Sobolev Trace Inequality Figalli and Y

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:06.031509Z

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Observation 9658409a-2f3e-4e4b-b29d-70fc22cb4ea5 · outbound

This paper cites G´ erard,Description du d´ efaut de compacit´ e de l’injection de Sobolev, ESAIM Control Optim.

Sharp Gradient Stability for the Sobolev Trace Inequality G´ erard,Description du d´ efaut de compacit´ e de l’injection de Sobolev, ESAIM Control Optim

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:06.195567Z

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Observation c7df7524-8705-490b-8ac1-193c40cf501f · outbound

This paper cites an unresolved cited work.

Sharp Gradient Stability for the Sobolev Trace Inequality Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:06.341170Z

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Unavailable: canonical work link unavailable.

Observation 39650625-457f-41ff-8531-7e1d5d5f6eac · outbound

This paper cites Hu and H.

Sharp Gradient Stability for the Sobolev Trace Inequality Hu and H

Reference 22

Resolution: malformed identifier; no resolver link, observed 2026-08-01T17:42:06.514677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e63c9741-e731-4647-a011-13d1c04561b0 · outbound

This paper cites an unresolved cited work.

Sharp Gradient Stability for the Sobolev Trace Inequality Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:06.737622Z

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Observation 7156db57-8f2f-433d-87db-40da83765ada · outbound

This paper cites Kato,Perturbation Theory for Linear Operators, Classics in Mathematics, Springer, Berlin, 1995.

Sharp Gradient Stability for the Sobolev Trace Inequality Kato,Perturbation Theory for Linear Operators, Classics in Mathematics, Springer, Berlin, 1995

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:06.912839Z

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Observation 60d0a9d9-e8fe-40de-be6d-966e58cd38d2 · outbound

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

Sharp Gradient Stability for the Sobolev Trace Inequality Lions,The concentration-compactness principle in the calculus of variations

Reference 25

Resolution: malformed identifier; no resolver link, observed 2026-08-01T17:42:07.051630Z

Source-reported events for the cited work

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Observation 906fffb8-8c6d-468e-ad9b-87bbdffe0ada · outbound

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

Sharp Gradient Stability for the Sobolev Trace Inequality Lions,The concentration-compactness principle in the calculus of variations

Reference 26

Resolution: verified exact; doi, observed 2026-08-01T17:43:22.845029Z

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 1d171320-4170-492d-ba18-10aad2da6e43 · outbound

This paper cites Lions and E.

Sharp Gradient Stability for the Sobolev Trace Inequality Lions and E

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:07.387609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4b028f6-cbd8-45be-9b92-62d121939166 · outbound

This paper cites an unresolved cited work.

Sharp Gradient Stability for the Sobolev Trace Inequality Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-08-01T17:43:22.714198Z

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 6744673d-7fb1-4f64-bf8f-42ee0dcbfb7c · outbound

This paper cites Maggi and R.

Sharp Gradient Stability for the Sobolev Trace Inequality Maggi and R

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:07.684826Z

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Unavailable: canonical work link unavailable.

Observation 425c1c83-67aa-484b-989e-c1734c0b57a1 · outbound

This paper cites Nazaret,Best constant in Sobolev trace inequalities on the half-space, Nonlinear Anal.65(2006), no.

Sharp Gradient Stability for the Sobolev Trace Inequality Nazaret,Best constant in Sobolev trace inequalities on the half-space, Nonlinear Anal.65(2006), no

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:07.817079Z

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Unavailable: canonical work link unavailable.

Observation 1421d541-6195-4078-a958-68f46ab1030c · outbound

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

Sharp Gradient Stability for the Sobolev Trace Inequality Neumayer,A note on strong-form stability for the Sobolev inequality, Calc

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:07.950775Z

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Observation 606ad657-e258-4bf6-ad85-a1ff0d2bf43d · outbound

This paper cites Ou,Positive harmonic functions on the upper half space satisfying a nonlinear boundary condition, Differential Integral Equations9(1996), no.

Sharp Gradient Stability for the Sobolev Trace Inequality Ou,Positive harmonic functions on the upper half space satisfying a nonlinear boundary condition, Differential Integral Equations9(1996), no

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:08.038647Z

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Observation d49fcc4e-5321-4aa1-af69-46d01cfa4093 · outbound

This paper cites Palatucci and A.

Sharp Gradient Stability for the Sobolev Trace Inequality Palatucci and A

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:08.156800Z

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Unavailable: canonical work link unavailable.

Observation b4268a7c-4649-404c-97a7-d0b74d1cc557 · outbound

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

Sharp Gradient Stability for the Sobolev Trace Inequality Solimini,A note on compactness-type properties with respect to Lorentz norms of bounded sub- sets of a Sobolev space, Ann

Reference 34

Resolution: verified exact; doi, observed 2026-08-01T17:43:22.633933Z

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 73465309-f79b-46ad-a34e-bf321989e6ec · outbound

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

Sharp Gradient Stability for the Sobolev Trace Inequality Struwe,A global compactness result for elliptic boundary value problems involving limiting nonlin- earities, Math

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:08.479764Z

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Observation ee809e47-61c2-4968-bd8b-f06b8a67b656 · outbound

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

Sharp Gradient Stability for the Sobolev Trace Inequality Talenti,Best constant in Sobolev inequality, Ann

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:08.639796Z

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Unavailable: canonical work link unavailable.

Observation 9d1ef73f-135f-4ee0-92f7-f7b8f0b513fa · outbound

This paper cites Teschl,Mathematical Methods in Quantum Mechanics: With Applications to Schr¨ odinger Opera- tors, 2nd ed., Graduate Studies in Mathematics, vol.

Sharp Gradient Stability for the Sobolev Trace Inequality Teschl,Mathematical Methods in Quantum Mechanics: With Applications to Schr¨ odinger Opera- tors, 2nd ed., Graduate Studies in Mathematics, vol

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:08.793844Z

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Observation 2f20f652-9840-4979-a4b6-6fd36ffdf01b · outbound

This paper cites Tintarev and K.-H.

Sharp Gradient Stability for the Sobolev Trace Inequality Tintarev and K.-H

Reference 38

Resolution: malformed identifier; doi_truncated, observed 2026-08-01T17:43:22.512566Z

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 84ff05d4-1db9-4212-bc6a-522fa8b28607 · outbound

This paper cites Zhang, Y.

Sharp Gradient Stability for the Sobolev Trace Inequality Zhang, Y

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:09.063654Z

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Unavailable: canonical work link unavailable.

Observation 74a8f1bd-6620-4ce8-9be1-b2e0b0d68dfc · outbound

This paper cites Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality.

Sharp Gradient Stability for the Sobolev Trace Inequality Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:09.174051Z

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Unavailable: canonical work link unavailable.

Observation 487a5f20-9ece-4de4-b2cc-da5d03af76a7 · outbound

This paper cites Zettl,Sturm–Liouville Theory, Mathematical Surveys and Monographs, vol.

Sharp Gradient Stability for the Sobolev Trace Inequality Zettl,Sturm–Liouville Theory, Mathematical Surveys and Monographs, vol

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-01T17:42:09.293429Z

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Pith citing papers

Observation 2a1ac650-b55e-43dc-82c8-0c2033257e1b · inbound

Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality cites this paper.

Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality Sharp Gradient Stability for the Sobolev Trace Inequality

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T07:34:56.464823Z

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Unavailable: canonical work link unavailable.