Robust nonlocal trace and extension theorems

2023/05/09 by Grube, Florian, Kassmann, Moritz
#35A15 #35J25 #35J60 #45G05 #46E35 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.05735

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.

Related

• Robust nonlocal trace spaces and Neumann problems
• Extension and trace for nonlocal operators
• Function spaces and extension results for nonlocal Dirichlet problems
• Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization
• Nonlocal operators of order near zero