by Kyril Tintarev (Uppsala University, Sweden) & Karl-Heinz Fieseler (Uppsala University, Sweden)

Table of Contents (107k)
Preface (118k)
Chapter 1: Functional spaces and convergence (787k)

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.

• Functional Spaces and Convergence
• Sobolev Spaces
• Weak Convergence Decomposition
• Concentration Compactness with Euclidean Shifts
• Concentration Compactness with Dilations
• Minimax Problems
• Differentiable Manifolds
• Riemannian Manifolds and Lie Groups
• Sobolev Spaces on Manifolds and Subelliptic Problems
• Further Applications