Zaremba problem with degenerate weights
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914733059211264 |
|---|---|
| author | Balci, Anna Kh. Lee, Ho-Sik |
| author_facet | Balci, Anna Kh. Lee, Ho-Sik |
| contents | We establish Zaremba problem for Laplacian and $p$-Laplacian with degenerate weights when the Dirichlet condition is only imposed in a set of positive weighted capacity. We prove weighted Sobolev-Poincaré inequality with sharp scaling-invariant constants involving weighted capacity. Then we show higher integrability of the gradient of the solution (Meyers estimate) with minimal conditions on the part of the boundary where the Dirichlet condition is assumed. Our results are new both for the linear $p=2$ and nonlinear case and include problems with the weight not only as a measure but also as a multiplier of the gradient of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zaremba problem with degenerate weights Balci, Anna Kh. Lee, Ho-Sik Analysis of PDEs We establish Zaremba problem for Laplacian and $p$-Laplacian with degenerate weights when the Dirichlet condition is only imposed in a set of positive weighted capacity. We prove weighted Sobolev-Poincaré inequality with sharp scaling-invariant constants involving weighted capacity. Then we show higher integrability of the gradient of the solution (Meyers estimate) with minimal conditions on the part of the boundary where the Dirichlet condition is assumed. Our results are new both for the linear $p=2$ and nonlinear case and include problems with the weight not only as a measure but also as a multiplier of the gradient of the solution. |
| title | Zaremba problem with degenerate weights |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.19813 |