Anisotropic symmetrization, convex bodies, and isoperimetric inequalities
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913633465794560 |
|---|---|
| author | Bianchi, Gabriele Cianchi, Andrea Gronchi, Paolo |
| author_facet | Bianchi, Gabriele Cianchi, Andrea Gronchi, Paolo |
| contents | This work is concerned with a Pólya-Szegö type inequality for anisotropic functionals of Sobolev functions. The relevant inequality entails a double-symmetrization involving both trial functions and functionals. A new approach that uncovers geometric aspects of the inequality is proposed. It relies upon anisotropic isoperimetric inequalities, fine properties of Sobolev functions, and results from the Brunn-Minkowski theory of convex bodies. Importantly, unlike previously available proofs, the one offered in this paper does not require approximation arguments and hence allows for a characterization of extremal functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anisotropic symmetrization, convex bodies, and isoperimetric inequalities Bianchi, Gabriele Cianchi, Andrea Gronchi, Paolo Functional Analysis Metric Geometry 46E35, 52A20 This work is concerned with a Pólya-Szegö type inequality for anisotropic functionals of Sobolev functions. The relevant inequality entails a double-symmetrization involving both trial functions and functionals. A new approach that uncovers geometric aspects of the inequality is proposed. It relies upon anisotropic isoperimetric inequalities, fine properties of Sobolev functions, and results from the Brunn-Minkowski theory of convex bodies. Importantly, unlike previously available proofs, the one offered in this paper does not require approximation arguments and hence allows for a characterization of extremal functions. |
| title | Anisotropic symmetrization, convex bodies, and isoperimetric inequalities |
| topic | Functional Analysis Metric Geometry 46E35, 52A20 |
| url | https://arxiv.org/abs/2411.01290 |