Stability of complement value problems for p-Lévy operators

Research output: Preprint/documentation/reportPreprint

Abstract

We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear integrodifferential $p$-L\'evy operators. A prototypical example of integrodifferential $p$-L\'evy operators is the well-known fractional $p$-Laplace operator. Our main focus is on nonlinear IDEs in the presence of Dirichlet, Neumann and Robin conditions and we show well-posedness results. Several results are new even for the fractional $p$-Laplace operator but we develop the approach for general translation-invariant nonlocal operators. We also bridge a gap from nonlocal to local, by showing that solutions to the local Dirichlet and Neumann boundary value problems associated with $p$-Laplacian are strong limits of the nonlocal ones.

Details

Original languageEnglish
Number of pages65
Publication statusPublished - 7 Mar 2023
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Keywords

Keywords

  • math.AP, 35D30, 35B35, 35J60, 35J66