Preprint
Boundary pointwise regularity for the divergence form elliptic boundary problem on uniform domain
ArXiv.org
Cornell University
09/22/2025
DOI: 10.48550/arxiv.2509.17690
Abstract
In this paper, we study the boundary pointwise regularity for the divergence form elliptic boundary problem. In generality, it is not convenient to define weak solutions for nonzero boundary data on domain with the rough boundary, e.g. uniform domain. However, in this paper, we introduce a definition of weak solutions for the boundary problem on uniform domain. What is interesting is that this definition can be considered to analysis the regularity of weak solutions. In particular, by establishing the energy inequality, we show the boundary pointwise Cα regularity by using compactness methods under the admissible condition. Furthermore, by establishing the linear property of solutions with respective to the harmonic functions, we also prove the boundary pointwise C1,α and C2,α regularities if the boundary data and the boundary of domain are pointwise C1,α and C2,α respectively.
Details
- Title: Subtitle
- Boundary pointwise regularity for the divergence form elliptic boundary problem on uniform domain
- Creators
- Tianyu GuanLihe WangChunqin Zhou
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2509.17690
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 09/22/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984966543302771
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