The Dirichlet problem for the $p(x)$-Laplacian with unbounded exponent $p(x)$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914809091457024 |
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| author | Khamsi, M. Lang, J. Mendez, O. Nekvinda, A. |
| author_facet | Khamsi, M. Lang, J. Mendez, O. Nekvinda, A. |
| contents | We prove the solvability of the Dirichlet problem for the variable exponent $p$-Laplacian with boundary data in $W^{1,p(x)}(Ω)$ on a bounded, smooth domain $Ω\subset {\mathbb R}^n$. Our main focus will be on an a.e. finite variable exponent $p(\cdot)$ with $n < \inf\limits_{x\in Ω}p(x)$ and $\sup\limits_{x\in Ω}p(x) = \infty$ under the sole assumption that $p\in C(Ω)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_10364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Dirichlet problem for the $p(x)$-Laplacian with unbounded exponent $p(x)$ Khamsi, M. Lang, J. Mendez, O. Nekvinda, A. Analysis of PDEs Functional Analysis We prove the solvability of the Dirichlet problem for the variable exponent $p$-Laplacian with boundary data in $W^{1,p(x)}(Ω)$ on a bounded, smooth domain $Ω\subset {\mathbb R}^n$. Our main focus will be on an a.e. finite variable exponent $p(\cdot)$ with $n < \inf\limits_{x\in Ω}p(x)$ and $\sup\limits_{x\in Ω}p(x) = \infty$ under the sole assumption that $p\in C(Ω)$. |
| title | The Dirichlet problem for the $p(x)$-Laplacian with unbounded exponent $p(x)$ |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2402.10364 |