A general framework for nonlocal Neumann problems
Guy Foghem, Moritz Kaßmann
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 exterior 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.
Topics & Concepts
Neumann boundary conditionVon Neumann architectureMathematicsApplied mathematicsMathematical analysisCalculus (dental)PhysicsBoundary value problemPure mathematicsMedicineDentistryDifferential Equations and Boundary ProblemsSpectral Theory in Mathematical PhysicsNumerical methods in inverse problems