Robust nonlocal trace and extension theorems

Abstract

We prove trace and extension results for Sobolev-type function spaces that are well suited for nonlocal Dirichlet and Neumann problems including those for the fractional $p$-Laplacian. Our results are robust with respect to the order of differentiability. In this sense they are in align with the classical trace and extension theorems.

In the updated version we fixed some irritating typos

References in corpus (4)

• A general framework for nonlocal Neumann problems
• On density of compactly supported smooth functions in fractional Sobolev spaces
• A Remake of Bourgain-Brezis-Mironescu Characterization of Sobolev Spaces
• Sharp weighted fractional Hardy inequalities