Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.15949 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910400952401920 |
|---|---|
| author | Goffi, Alessandro Leonori, Tommaso |
| author_facet | Goffi, Alessandro Leonori, Tommaso |
| contents | This work addresses the problem of (global) maximal regularity for quasilinear evolution equations with sublinear gradient growth and right-hand side in Lebesgue spaces, complemented with Neumann boundary conditions. The proof relies on a suitable variation of the Bernstein technique and the Bochner identity, and provides new results even for the simpler parabolic $p$-Laplacian equation with unbounded source term. As a byproduct we also obtain a second-order estimate that can be of independent interest when the right-side of the equation belongs to $L^m$, $m\neq 2$. This approach leads to new results even for stationary problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15949 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On maximal regularity estimates for quasilinear evolution equations via the integral Bernstein method Goffi, Alessandro Leonori, Tommaso Analysis of PDEs This work addresses the problem of (global) maximal regularity for quasilinear evolution equations with sublinear gradient growth and right-hand side in Lebesgue spaces, complemented with Neumann boundary conditions. The proof relies on a suitable variation of the Bernstein technique and the Bochner identity, and provides new results even for the simpler parabolic $p$-Laplacian equation with unbounded source term. As a byproduct we also obtain a second-order estimate that can be of independent interest when the right-side of the equation belongs to $L^m$, $m\neq 2$. This approach leads to new results even for stationary problems. |
| title | On maximal regularity estimates for quasilinear evolution equations via the integral Bernstein method |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.15949 |