Sharp quantitative Talenti's inequality in particular cases
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908990362877952 |
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| author | Acampora, Paolo Lamboley, Jimmy |
| author_facet | Acampora, Paolo Lamboley, Jimmy |
| contents | In this paper, we focus on the famous Talenti's symmetrization inequality, more precisely its $L^p$ corollary asserting that the $L^p$-norm of the solution to $-Δv=f^\sharp$ is higher than the $L^p$-norm of the solution to $-Δu=f$ (we are considering Dirichlet boundary conditions, and $f^\sharp$ denotes the Schwarz symmetrization of $f:Ω\to\mathbb{R}_+$). We focus on the particular case where functions $f$ are defined on the unit ball, and are characteristic functions of a subset of this unit ball. We show in this case that stability occurs for the $L^p$-Talenti inequality with the sharp exponent 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp quantitative Talenti's inequality in particular cases Acampora, Paolo Lamboley, Jimmy Analysis of PDEs 35j25, 25p15, 49q10, 49k20, 49k30, 49k90 In this paper, we focus on the famous Talenti's symmetrization inequality, more precisely its $L^p$ corollary asserting that the $L^p$-norm of the solution to $-Δv=f^\sharp$ is higher than the $L^p$-norm of the solution to $-Δu=f$ (we are considering Dirichlet boundary conditions, and $f^\sharp$ denotes the Schwarz symmetrization of $f:Ω\to\mathbb{R}_+$). We focus on the particular case where functions $f$ are defined on the unit ball, and are characteristic functions of a subset of this unit ball. We show in this case that stability occurs for the $L^p$-Talenti inequality with the sharp exponent 2. |
| title | Sharp quantitative Talenti's inequality in particular cases |
| topic | Analysis of PDEs 35j25, 25p15, 49q10, 49k20, 49k30, 49k90 |
| url | https://arxiv.org/abs/2503.07337 |