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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.
Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volum
Concentration compactness methods are applied to PDE's that lack compactness properties, typically due to the scaling invariance of the underlying problem. This
Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volum
Wave maps are the simplest wave equations taking their values in a Riemannian manifold $(M,g)$. Their Lagrangian is the same as for the scalar equation, the onl
This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic t
