Pith Number

pith:Q75ATBAE

pith:2026:Q75ATBAELYSLIVT3ZGEGSGPA4P

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Failure of Calder\'{o}n-Zygmund estimates for degenerate elliptic PDEs with $A_p$-weights when $p > 2$

Armin Schikorra, Martin Ulmer

Convex integration constructs examples showing weighted Calderón-Zygmund estimates fail for degenerate linear elliptic PDEs with A_p weights when p > 2.

arxiv:2605.15414 v1 · 2026-05-14 · math.AP

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Claims

C1strongest claim

We use convex integration techniques to provide examples of failure of weighted Calderón-Zygmund estimates for degenerate linear elliptic PDEs when the weights are in A_p, p > 2.

C2weakest assumption

The construction assumes that suitable degenerate coefficients and A_p weights for p > 2 exist such that convex integration produces a solution violating the weighted estimate (abstract).

C3one line summary

Constructs counterexamples via convex integration demonstrating failure of weighted Calderón-Zygmund estimates for degenerate linear elliptic PDEs with A_p-weights when p > 2.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] K. Astala, D. Faraco, and L. Sz´ ekelyhidi, Jr. Convex integration and theLp theory of elliptic equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 7(1):1–50, 2008. 2 2008

[2] A. K. Balci, L. Diening, R. Giova, and A. Passarelli di Napoli. Elliptic equations with degenerate weights.SIAM J. Math. Anal., 54(2):2373–2412, 2022. 2, 20 2022

[3] S.-S. Byun and L. Wang. Elliptic equations with BMO coefficients in Reifenberg do- mains.Communications on Pure and Applied Mathematics, 57(10):1283–1310, 2004. eprint: https://onlinelibrary.wiley.com 2004 · doi:10.1002/cpa.20037

[4] S.-S. Byun, L. Wang, and S. Zhou. Nonlinear elliptic equations with BMO coefficients in Reifenberg domains.Journal of Functional Analysis, 250(1):167–196, Sept. 2007. 2 2007

[5] D. Cao, T. Mengesha, and T. Phan. Weighted-W 1,p estimates for weak solutions of degenerate and singular elliptic equations.Indiana Univ. Math. J., 67(6):2225–2277, 2018. 2 2018

Receipt and verification

First computed	2026-05-20T00:00:57.372856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87fa0984045e24b4567bc9886919e0e3e387c1384a763f5b3e86f656626e5669

Aliases

arxiv: 2605.15414 · arxiv_version: 2605.15414v1 · doi: 10.48550/arxiv.2605.15414 · pith_short_12: Q75ATBAELYSL · pith_short_16: Q75ATBAELYSLIVT3 · pith_short_8: Q75ATBAE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q75ATBAELYSLIVT3ZGEGSGPA4P \
  | 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: 87fa0984045e24b4567bc9886919e0e3e387c1384a763f5b3e86f656626e5669

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-14T20:58:15Z",
    "title_canon_sha256": "e2d02972b26d693272eccf1f85ab86b6c189816840afbf3f5bf75eb0a5aef53a"
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