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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.00184 |
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| _version_ | 1866914340333944832 |
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| author | Colesanti, Andrea Qin, Lei Salani, Paolo |
| author_facet | Colesanti, Andrea Qin, Lei Salani, Paolo |
| contents | We prove a Brunn-Minkowski type inequality for the first (nontrivial) Dirichlet eigenvalue of the weighted $p$-operator \[ -Δ_{p,γ}u=-\text{div}(|\nabla u|^{p-2} \nabla u)+(x,\nabla u)|\nabla u|^{p-2}, \] where $p>1$, in the class of bounded Lipschitz domains in $\mathbb{R}^n$. We also prove that any corresponding positive eigenfunction is log-concave if the domain is convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric properties of solutions to elliptic PDE's in Gauss space and related Brunn-Minkowski type inequalities Colesanti, Andrea Qin, Lei Salani, Paolo Analysis of PDEs We prove a Brunn-Minkowski type inequality for the first (nontrivial) Dirichlet eigenvalue of the weighted $p$-operator \[ -Δ_{p,γ}u=-\text{div}(|\nabla u|^{p-2} \nabla u)+(x,\nabla u)|\nabla u|^{p-2}, \] where $p>1$, in the class of bounded Lipschitz domains in $\mathbb{R}^n$. We also prove that any corresponding positive eigenfunction is log-concave if the domain is convex. |
| title | Geometric properties of solutions to elliptic PDE's in Gauss space and related Brunn-Minkowski type inequalities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.00184 |