Work

Stability of complement value problems for p-Lévy operators

Year: 2024

Type: article

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.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-024-01006-6

Author: Guy Foghem

Institution: Technische Universität Dresden

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, Technische Universität Dresden, Universität Bielefeld