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.

arXiv commentIn the updated version we fixed some irritating typos

References in corpus (7)

• Local behavior of fractional $p$-minimizers
• Fractional Laplacians on domains, a development of Hörmander's theory of mu-transmission pseudodifferential operators
• A general framework for nonlocal Neumann problems
• Finite element approximations of the nonhomogeneous fractional Dirichlet problem
• 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