Fractional Sobolev logarithmic inequalities

Fuente: arXiv
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Main Author: Sahu, Vivek
Format: Preprint
Published: 2025
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author Sahu, Vivek
author_facet Sahu, Vivek
contents We establish new Euclidean Sobolev logarithmic inequalities in the framework of fractional Sobolev spaces and their weighted version. Our approach relies on a interpolation inequality, which can be viewed as a fractional Caffarelli-Kohn-Nirenberg type inequality. We further relate the optimal constant in this interpolation inequality to a corresponding variational problem. These results extend classical Sobolev logarithmic inequalities to the nonlocal Euclidean framework and provide new tools for analysis in fractional Sobolev spaces.
format Preprint
id arxiv_https___arxiv_org_abs_2509_07559
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fractional Sobolev logarithmic inequalities
Sahu, Vivek
Analysis of PDEs
46E35, 26D15, 26A33
We establish new Euclidean Sobolev logarithmic inequalities in the framework of fractional Sobolev spaces and their weighted version. Our approach relies on a interpolation inequality, which can be viewed as a fractional Caffarelli-Kohn-Nirenberg type inequality. We further relate the optimal constant in this interpolation inequality to a corresponding variational problem. These results extend classical Sobolev logarithmic inequalities to the nonlocal Euclidean framework and provide new tools for analysis in fractional Sobolev spaces.
title Fractional Sobolev logarithmic inequalities
topic Analysis of PDEs
46E35, 26D15, 26A33
url https://arxiv.org/abs/2509.07559