C^2s regularity for fully nonlinear nonlocal equations with bounded right hand side

2019/07/04 by Hernán Vivas, Vivas, Hernán
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1907.02455

openalex publication_date 2019/07/04 · openalex created_date 2019/07/12 · openalex updated_date 2026/07/28

Abstract

We establish sharp C^2s interior regularity estimates for solutions of fully nonlinear nonlocal equations with bounded right hand side. More precisely, we show that if I is a fully nonlinear nonlocal concave or convex elliptic operator and f∈ L^∞(B₁) then Iu=f \textrm in B₁ ⇒ u∈ C^2s(B_1/2). This result generalizes the linear counterpart proved by Ros-Oton and Serra and extends previous available results for fully nonlinear nonlocal operators. As an application, we get a basic regularity estimate for the nonlocal two membranes problem.

Citations

• The Evans-Krylov theorem for nonlocal fully nonlinear equations

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