A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method

Alessandro Goffi

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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.
Original languageEnglish (US)
JournalBolletino dell Unione Matematica Italiana
DOIs
StatePublished - Nov 5 2022
Externally publishedYes

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