Sobolev inequalities, rearrangements, isoperimetry and interpolation spaces
Joaquim Martin, Mario Milman
TL;DR
This paper explores the relationships between Sobolev inequalities, rearrangement inequalities, isoperimetric inequalities, and interpolation spaces within metric spaces, providing a unified characterization of Poincaré inequalities.
Contribution
It offers a new characterization of Poincaré inequalities in metric spaces through rearrangement inequalities, linking various fundamental inequalities in analysis.
Findings
Unified framework for Poincaré inequalities in metric spaces
Connections established between isoperimetry and rearrangement inequalities
Enhanced understanding of interpolation spaces in the context of Sobolev inequalities
Abstract
We characterize Poincar\'{e} inequalities in metric spaces using rearrangement inequalities
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Taxonomy
TopicsNonlinear Partial Differential Equations