A general framework for nonlocal Neumann problems

Abstract

Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains with prescribed conditions on the complement of the domain. Our main focus is on the inhomogeneous Neumann problem in a rather general setting. We also study the transition from complement value problems to local boundary value problems. Several results are new even for the fractional Laplace operator. The setting also covers relevant models in the framework of peridynamics.

Published in Commun. Math. Sci.: https://dx.doi.org/10.4310/CMS.2024.v22.n1.a2

References in corpus (8)

• On density of compactly supported smooth functions in fractional Sobolev spaces
• A Remake of Bourgain-Brezis-Mironescu Characterization of Sobolev Spaces
• On density of smooth functions in weighted fractional Sobolev spaces
• The divergence theorem and nonlocal counterparts
• The nonlocal Neumann problem
• Nonlocal Gagliardo-Nirenberg-Sobolev type inequality
• Robust nonlocal trace spaces and Neumann problems
• Stability of complement value problems for $p$-Lévy operators

Cited by in corpus (4)

• Nonlocal complement value problem for a global in time parabolic equation
• The divergence theorem and nonlocal counterparts
• The Neumann condition for the superposition of fractional Laplacians
• Robust nonlocal trace and extension theorems