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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
classification math.AP
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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  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.

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