Stability of complement value problems for p-Lévy operators

Abstract We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear nonlocal integro-differential p -Lévy operators. A prototypical example of integro-differential p -Lévy operators is the well-known fractional p -Laplace operator. Our main focus is on nonlinear integro-differential equations 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 the 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.