Robust nonlocal trace and extension theorems

Grube, Florian; Kassmann, Moritz

doi:10.2140/apde.2025.18.2367

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Robust nonlocal trace and extension theorems

Florian Grube and Moritz Kassmann

Vol. 18 (2025), No. 10, 2367–2414

DOI: 10.2140/apde.2025.18.2367

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 align with the classical trace and extension theorems.

Keywords

nonlocal Sobolev space, trace, extension, convergence of trace space

Mathematical Subject Classification

Primary: 35J25, 35J60, 45G05, 46E35, 47G20

Secondary: 35A15

Milestones

Received: 22 December 2023

Revised: 2 October 2024

Accepted: 8 January 2025

Published: 4 November 2025

Authors

Florian Grube
Fakultät für Mathematik Universität Bielefeld Bielefeld Germany

Moritz Kassmann
Fakultät für Mathematik Universität Bielefeld Bielefeld Germany

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Vol. 18, No. 10, 2025