On maximal regularity estimates for quasilinear evolution equations via the integral Bernstein method

Alessandro Goffi; Tommaso Leonori

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arXiv · 2310.15949

On maximal regularity estimates for quasilinear evolution equations via the integral Bernstein method

Alessandro Goffi·Tommaso Leonori

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Abstract

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.

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Alessandro Goffi, Tommaso Leonori. 2023-10-24. On maximal regularity estimates for quasilinear evolution equations via the integral Bernstein method. https://arxiv.org/abs/2310.15949

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