A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method
Analysis of PDEs
2022-08-01 v1
Abstract
We establish a priori Lipschitz estimates for equations with mixed local and nonlocal diffusion, coercive gradient terms and unbounded right-hand side in Lebesgue spaces through an integral refinement of the Bernstein method. This relies on a nonlinear, nonlocal and variational version of the Bochner identity that involves the adjoint equation of the linearization of the initial problem.
Cite
@article{arxiv.2207.14587,
title = {A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method},
author = {Alessandro Goffi},
journal= {arXiv preprint arXiv:2207.14587},
year = {2022}
}
Comments
14 pages