Published March 20, 2025 | Version Published
Journal Article Open

On the sharp constants in the regional fractional Sobolev inequalities

  • 1. ROR icon Ludwig-Maximilians-Universität München
  • 2. Munich Center for Quantum Science and Technology
  • 3. ROR icon California Institute of Technology
  • 4. ROR icon Hong Kong University of Science and Technology
  • 5. ROR icon Peking University

Abstract

In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.

Copyright and License

© The Author(s) 2025. 

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Funding

R. L. F. was partially supported by the US National Science Foundation grant DMS-1954995 and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Germany’s Excellence Strategy EXC-2111-390814868. T. J. was partially supported by NSFC 12122120 and Hong Kong RGC grant GRF 16302519.

Open access funding provided by Hong Kong University of Science and Technology.

Data Availability

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Additional Information

This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

Files

s42985-025-00317-2.pdf

Files (381.7 kB)

Name Size Download all
md5:0648cddfa69ff0359296c3a2cc433383
381.7 kB Preview Download

Additional details

Related works

Describes
Journal Article: https://rdcu.be/ee4bM (URL)
Is new version of
Discussion Paper: arXiv:2403.00357 (arXiv)

Funding

National Science Foundation
DMS-1954995
Deutsche Forschungsgemeinschaft
EXC-2111-390814868
National Natural Science Foundation of China
12122120
University Grants Committee
16302519
Hong Kong University of Science and Technology

Dates

Accepted
2025-02-21

Caltech Custom Metadata

Caltech groups
Division of Physics, Mathematics and Astronomy (PMA)
Publication Status
Published