Concentration Compactness Functional-Analytic Theory of Concentration Phenomena - Tintarev, Kyril (De Gruyter Series in Nonlinear Analysis and Applications, 2020)
Concentration compactness methods are applied to PDE's that lack compactness properties, typically due to the scaling invariance of the underlying problem. This monograph presents a systematic functional-analytic presentation of concentration mechanisms and is by far the most extensive and systematic collection of mathematical tools for analyzing the convergence of functional sequences via the mechanism of concentration.