Fine boundary regularity for fully nonlinear mixed local-nonlocal problems

2023/01/06 by Mitesh Modasiya, Modasiya, Mitesh, Abhrojyoti Sen +1
Mathematics · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2301.02397

Abstract

We consider Dirichlet problems for fully nonlinear mixed local-nonlocal non-translation invariant operators. For a bounded C² domain Ω⊂ ℝ^d, let u∈ C(ℝ^d) be a viscosity solution of such Dirichlet problem. We obtain global Lipschitz regularity and fine boundary regularity for u by constructing appropriate sub and supersolutions coupled with a Harnack type inequality. We apply these results to obtain Hölder regularity of Du up to the boundary.

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