Existence of weak solutions for the anisotropic $p(x)$-Laplacian via degree theory
| Title: | Existence of weak solutions for the anisotropic $p(x)$-Laplacian via degree theory |
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| Authors: | Ochoa, Pablo, Silva, Analía, Valverde, Federico |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Analysis of PDEs, 35A16, 35D30, 35J60, 47H11 |
| More Details: | In this paper, we consider Dirichlet boundary value problem involving the anisotropic $p(x)$-Laplacian, where $p(x)= (p_1(x), ..., p_n(x))$, with $p_i(x)> 1$ in $\overline{\Omega}$. Using the topological degree constructed by Berkovits, we prove, under appropriate assumptions on the data, the existence of weak solutions for the given problem. An important contribution is that we are considering the degenerate and the singular cases in the discussion. Finally, according to the compact embedding for anisotropic Sobolev spaces, we point out that the considered boundaru value problem may be critical in some region of $\Omega$. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2411.03123 |
| Accession Number: | edsarx.2411.03123 |
| Database: | arXiv |
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