On widely degenerate \textit{p}-Laplace equations with symmetric data
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909231439937536 |
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| author | Russo, Stefania |
| author_facet | Russo, Stefania |
| contents | In this paper, we consider the Dirichlet problems with a widely degenerate equation. Through a well-known result by Talenti, we explicitly express the gradient of the solution $u_p$ outside the ball with a radius of $1$, if the datum $f$ is a non-negative radially decreasing function. This allows us to establish some sharp higher regularity results for the weak solutions, assuming that the datum $f$ belongs to a suitable Lorentz space, i.e. under a weaker assumption on the datum with respect to the available literature. Moreover we analyze the behaviour of $u_p$ as $p \to 1^+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On widely degenerate \textit{p}-Laplace equations with symmetric data Russo, Stefania Analysis of PDEs 35B65, 35J70, 35J75, 49K20 In this paper, we consider the Dirichlet problems with a widely degenerate equation. Through a well-known result by Talenti, we explicitly express the gradient of the solution $u_p$ outside the ball with a radius of $1$, if the datum $f$ is a non-negative radially decreasing function. This allows us to establish some sharp higher regularity results for the weak solutions, assuming that the datum $f$ belongs to a suitable Lorentz space, i.e. under a weaker assumption on the datum with respect to the available literature. Moreover we analyze the behaviour of $u_p$ as $p \to 1^+$. |
| title | On widely degenerate \textit{p}-Laplace equations with symmetric data |
| topic | Analysis of PDEs 35B65, 35J70, 35J75, 49K20 |
| url | https://arxiv.org/abs/2403.11315 |