Hardy-Littlewood-Sobolev and related inequalities: stability
Jean Dolbeault, Maria J. Esteban
TL;DR
This paper reviews existing stability results for Sobolev, Hardy-Littlewood-Sobolev, and related inequalities, and offers new insights on constructive stability estimates for HLS inequalities.
Contribution
It provides a comprehensive review and introduces new observations on constructive stability estimates for Hardy-Littlewood-Sobolev inequalities.
Findings
Summarizes current stability results for key inequalities
Provides new constructive stability estimates for HLS inequalities
Enhances understanding of inequality stability mechanisms
Abstract
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive stability estimates for (HLS).
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Taxonomy
TopicsNonlinear Partial Differential Equations · Numerical methods in engineering · Differential Equations and Boundary Problems