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Optimal Boundary Regularity for Uniformly Degenerate Elliptic Equations

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arxiv 2411.16418 v1 pith:MGIPH6RQ submitted 2024-11-25 math.AP

Qing Han , Jiongduo Xie This is my paper · ORCID
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keywords boundarydegenerateellipticequationsoptimalregularitysolutionsuniformly
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In this survey paper, we study the optimal regularity of solutions to uniformly degenerate elliptic equations in bounded domains and establish the H\"older continuity of solutions and their derivatives up to the boundary.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Schauder estimates for elliptic equations degenerating on lower dimensional manifolds

    math.AP 2025-01 conditional novelty 7.0 of 10

    Weak solutions to weighted elliptic equations with a distance-to-a-manifold weight are shown to be C^{0,α} or C^{1,α} up to the characteristic manifold under a homogeneous conormal condition.

  2. Sobolev estimates for parabolic and elliptic equations in divergence form with degenerate coefficients

    math.AP 2024-12 conditional novelty 7.0 of 10

    For degenerate parabolic and elliptic equations in divergence form on the upper half space, the paper establishes well-posedness and weighted mixed-norm Sobolev estimates under partially BMO coefficients.

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