Pith Number

pith:BBUPGF2O

pith:2026:BBUPGF2O4ARTO45CNKYZEEQENL

not attested not anchored not stored refs resolved

Ultracontractivity of Heat semigroups in $\mathrm{L}^{2}\left( \Omega \right)$ with non-local Robin boundary conditions using Nash's inequality

Christoph Schwerdt

Heat semigroups with generalized non-local Robin boundary conditions are ultracontractive on bounded Lipschitz domains.

arxiv:2605.13413 v1 · 2026-05-13 · math.AP · math.FA

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Claims

C1strongest claim

Ultracontractivity of the solution semigroup is shown by using Nash's inequality on the Sobolev space H1(Omega) under quite mild assumptions on B.

C2weakest assumption

The assumptions on the boundary operator B are 'quite mild' and the domain is bounded Lipschitz with uniform ellipticity of A; if these fail to hold in the stated generality, the Nash inequality application may not yield the ultracontractive bound.

C3one line summary

Heat semigroups with non-local Robin boundary conditions on Lipschitz domains in R^d (d>2) are ultracontractive in L2 via Nash inequality on H1(Omega).

References

30 extracted · 30 resolved · 0 Pith anchors

[1] Pitt , journal =

[2] Simader , journal =

[3] Ben de Pagter , journal =

[4] Tosio Kato , journal =

[5] El-Maati Ouhabaz , publisher =

Receipt and verification

First computed	2026-05-18T02:44:47.401965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0868f3174ee0233773a26ab19212046afd8b07a1e84ad83528b80fdaa7fb7c8a

Aliases

arxiv: 2605.13413 · arxiv_version: 2605.13413v1 · doi: 10.48550/arxiv.2605.13413 · pith_short_12: BBUPGF2O4ART · pith_short_16: BBUPGF2O4ARTO45C · pith_short_8: BBUPGF2O

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BBUPGF2O4ARTO45CNKYZEEQENL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0868f3174ee0233773a26ab19212046afd8b07a1e84ad83528b80fdaa7fb7c8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edfeb8be67249e8432da45cb804202d1c72957d0face2a48a9cf93d4eb0c59be",
    "cross_cats_sorted": [
      "math.FA"
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T12:09:11Z",
    "title_canon_sha256": "8cebb0bbb41d35a4b079603e38768e51a01e951ded291d92f828c6909adda749"
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  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}