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Hauptverfasser: Goffi, Alessandro, Leonori, Tommaso
Format: Preprint
Veröffentlicht: 2023
Schlagworte:
Online-Zugang:https://arxiv.org/abs/2310.15949
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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