Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

Michael Struwe (auth.)9780387112909, 0387112901

“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged editon appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces. This third, revised edition has been long awaited for by the mathematical community. It is now appearing in a completely updated and enlarged version with an additional chapter on the moment map by Prof. Frances Kirwan (Oxford) and a fully updated bibliography of work in this area. The book deals firstly with actions of algebraic groups on algebraic varieties, separating orbits by invariants and construction quotient spaces; and secondly with applications of this theory to the construction of moduli spaces. It is a systematic exposition of the geometric aspects of the classical theory of polynomial invariants.

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Table of contents :
Front Matter….Pages i-xviii
The Direct Methods in the Calculus of Variations….Pages 1-73
Minimax Methods….Pages 74-168
Limit Cases of the Palais-Smale Condition….Pages 169-236
Back Matter….Pages 237-274