Global gradient regularity and a Hopf lemma for quasilinear operators of mixed local-nonlocal type

2023/08/11 by Antonini, Carlo Alberto, Cozzi, Matteo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.06075

Abstract

We address some regularity issues for mixed local-nonlocal quasilinear operators modeled upon the sum of a p-Laplacian and of a fractional (s, q)-Laplacian. Under suitable assumptions on the right-hand sides and the outer data, we show that weak solutions of the Dirichlet problem are C^{1, θ}-regular up to the boundary. In addition, we establish a Hopf type lemma for positive supersolutions. Both results hold assuming the boundary of the reference domain to be merely of class C^{1, α}, while for the regularity result we also require that p > s q.

Cited by

• Interior C^1,α regularity of mixed local-nonlocal (p,q)-energy minimizers for p≤ sq

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