Pith Number

pith:5MPG26EK

pith:2023:5MPG26EKDGEQBSWLYNSJ7LNIRM

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Maximal $L^{q}$-regularity for the Laplacian on manifolds with edges

Nikolaos Roidos

An R-sectoriality perturbation technique for non-commuting operators in Bochner spaces yields maximal L^q-regularity for the Laplacian on manifolds with edges.

arxiv:2310.12578 v2 · 2023-10-19 · math.AP · math.FA

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Record completeness

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Claims

C1strongest claim

Based on this and on bounded H^∞-functional calculus results for the Laplacian on manifolds with conical singularities, we show maximal L^q-regularity for the Laplacian on manifolds with edge type singularities in appropriate weighted Sobolev spaces.

C2weakest assumption

The R-sectoriality perturbation technique for non-commuting operators defined in Bochner spaces is valid and can be combined with the existing bounded H^∞-functional calculus on conical singularities without additional obstructions arising from the edge geometry.

C3one line summary

Develops R-sectoriality perturbation for non-commuting operators to establish maximal L^q-regularity of the Laplacian on manifolds with edges and applies it to short-time well-posedness of the porous medium equation.

References

66 extracted · 66 resolved · 0 Pith anchors

[1] H. Amann. Compact embeddings of vector valued Sobolev and Besov space s. Glasnik Matematicki 35(55), no. 1, 161–177 (2000) 2000

[2] H. Amann. Linear and quasilinear parabolic problems, Vol. I Abstract linear theory. Monographs in Mathematics 89, Birkh¨ auser Verlag (1995) 1995

[3] H. Amann. Linear and quasilinear parabolic problems, Vol. II Functio n spaces . Monographs in Mathematics 106, Birkh¨ auser Verlag (2019) 2019

[4] H. Amann, M. Hieber, G. Simonett. Bounded H∞-calculus for elliptic operators . Diﬀerential Inte- gral Equations 7, no. 3–4, 613–653 (1994) 1994

[5] D. Aronson, L. Peletier. Large time behaviour of solutions of the porous medium equat ion in bounded domains. Journal of Diﬀerential Equations 39, no. 3, 378–412 (1981) 1981

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-28T02:04:38.808367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb1e6d788a198900cacbc3649fada88b086363af470737927e78a7dc017a743c

Aliases

arxiv: 2310.12578 · arxiv_version: 2310.12578v2 · doi: 10.48550/arxiv.2310.12578 · pith_short_12: 5MPG26EKDGEQ · pith_short_16: 5MPG26EKDGEQBSWL · pith_short_8: 5MPG26EK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5MPG26EKDGEQBSWLYNSJ7LNIRM \
  | 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: eb1e6d788a198900cacbc3649fada88b086363af470737927e78a7dc017a743c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca0eddb6424f3acb9f189d14b8240f73de94d989355c5fea0dc69724ca04a8c0",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-10-19T08:39:49Z",
    "title_canon_sha256": "17e7934b12e4c543167f7a78d95bb71c39e56bcb02477d60eb8e5451b697814a"
  },
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  "source": {
    "id": "2310.12578",
    "kind": "arxiv",
    "version": 2
  }
}