Calculus of Variations and Geometric Measure Theory

G. Foghem - M. Kassmann

A general framework for nonlocal Neumann problems

created by foghem on 09 Aug 2022



Inserted: 9 aug 2022
Last Updated: 9 aug 2022

Year: 2022

ArXiv: 2204.06793 PDF


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.

Tags: GeMeThNES