Journal article
Boundary pointwise regularity for the Poisson problem on uniform domain
Journal of Differential Equations, Vol.482, 114686
11/25/2026
DOI: 10.1016/j.jde.2026.114686
Abstract
In this paper, we study the boundary pointwise regularity for the Poisson problem on domains with rough boundaries, specifically uniform domains. In general, it is not straightforward to define weak solutions for non-zero boundary data on such domains. To address this, we introduce a novel definition of weak solutions tailored to the setting of uniform domains. Remarkably, this definition allows for the analysis of the regularity of weak solutions. In particular, by establishing an energy inequality, we prove the boundary pointwise Cα regularity by using compactness methods under the admissible condition. Furthermore, by exploiting the linear structure of solutions with respect to the harmonic functions, we establish boundary pointwise C1,α and C2,α regularities when the boundary data and the domain boundary are pointwise C1,α and C2,α, respectively.
Details
- Title: Subtitle
- Boundary pointwise regularity for the Poisson problem on uniform domain
- Creators
- Tianyu Guan - Shanghai Jiao Tong UniversityLihe Wang - University of IowaChunqin Zhou - Shanghai Jiao Tong University
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.482, 114686
- DOI
- 10.1016/j.jde.2026.114686
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Publisher
- Elsevier Inc
- Grant note
- 24ZR1440700 / STCSM (https://doi.org/10.13039/501100003399) 12571223; 12031012 / NSFC (https://doi.org/10.13039/501100001809)
- Language
- English
- Date published
- 11/25/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985218381602771
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