$p(x)$-Stability of the Dirichlet problem for Poisson's equation with variable exponents
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909713628659712 |
|---|---|
| author | Rouhani, Behzad Djafari Mendez, Osvaldo |
| author_facet | Rouhani, Behzad Djafari Mendez, Osvaldo |
| contents | It is shown that if the sequence $(p_j(x))$ increases uniformly to $p(x)$ in a bounded, smooth domain $Ω$, then the sequence $(u_i)$ of solutions to the Dirichlet problem for the $p_i(x)$-Laplacian with fixed boundary datum $φ$ converges (in a sense to be made precise) to the solution $u_p$ of the Dirichlet problem for the $p(x)$-Laplacian with boundary datum $φ$. A similar result is proved for a decreasing sequence $p_j\searrow p$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $p(x)$-Stability of the Dirichlet problem for Poisson's equation with variable exponents Rouhani, Behzad Djafari Mendez, Osvaldo Analysis of PDEs It is shown that if the sequence $(p_j(x))$ increases uniformly to $p(x)$ in a bounded, smooth domain $Ω$, then the sequence $(u_i)$ of solutions to the Dirichlet problem for the $p_i(x)$-Laplacian with fixed boundary datum $φ$ converges (in a sense to be made precise) to the solution $u_p$ of the Dirichlet problem for the $p(x)$-Laplacian with boundary datum $φ$. A similar result is proved for a decreasing sequence $p_j\searrow p$ |
| title | $p(x)$-Stability of the Dirichlet problem for Poisson's equation with variable exponents |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.23417 |