Stability of complement value problems for $p$-L\'evy operators

Guy Foghem

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arXiv · 2303.03776

Stability of complement value problems for $p$-L\'evy operators

Guy Foghem

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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.

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Guy Foghem. 2023-03-07. Stability of complement value problems for $p$-L\'evy operators. https://arxiv.org/abs/2303.03776

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