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Concentration Compactness: Functional-analytic Grounds And Applications
Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces.Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.
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The book is very well written, the arguments are complete and many illustrative examples are given. It can be helpful to all: beginners as well as advanced researchers who want to deepen their knowledge and develop correct intuition about the topic discussed. -- Mathematical Reviews "Mathematical Reviews"