The $L_{p}$-Brunn-Minkowski inequalities for variational functionals with $0\leq p<1$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913925347409920 |
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| author | Hu, Jinrong |
| author_facet | Hu, Jinrong |
| contents | The infinitesimal forms of the $L_{p}$-Brunn-Minkowski inequalities for variational functionals, such as the $q$-capacity, the torsional rigidity, and the first eigenvalue of the Laplace operator, are investigated for $p \geq 0$. These formulations yield Poincaré-type inequalities related to these functionals. As an application, the $L_{p}$-Brunn-Minkowski inequalities for torsional rigidity with $0 \leq p < 1$ are confirmed for small $C^{2}$-perturbations of the unit ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20269 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $L_{p}$-Brunn-Minkowski inequalities for variational functionals with $0\leq p<1$ Hu, Jinrong Analysis of PDEs The infinitesimal forms of the $L_{p}$-Brunn-Minkowski inequalities for variational functionals, such as the $q$-capacity, the torsional rigidity, and the first eigenvalue of the Laplace operator, are investigated for $p \geq 0$. These formulations yield Poincaré-type inequalities related to these functionals. As an application, the $L_{p}$-Brunn-Minkowski inequalities for torsional rigidity with $0 \leq p < 1$ are confirmed for small $C^{2}$-perturbations of the unit ball. |
| title | The $L_{p}$-Brunn-Minkowski inequalities for variational functionals with $0\leq p<1$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.20269 |