English

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.

Keywords

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

R2 v1 2026-06-25T01:19:43.697Z