Self-dual partial differential systems and their variational principles

Nassif Ghoussoub

This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The applications, however, require a fair knowledge of classical analysis and PDEs which is needed to make judicious choices of function spaces where the self-dual variational principles need to be applied, and these choices necessarily require prior knowledge of the expected regularity of the (weak) solutions. While this text contains many new results, it is the author's hope that this material will soon become standard for all graduate students.

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  • Convex Analysis on Phase Space.- Legendre-Fenchel Duality on Phase Space.- Self-dual Lagrangians on Phase Space.- Skew-Adjoint Operators and Self-dual Lagrangians.- Self-dual Vector Fields and Their Calculus.- Completely Self-Dual Systems and their Lagrangians.- Variational Principles for Completely Self-dual Functionals.- Semigroups of Contractions Associated to Self-dual Lagrangians.- Iteration of Self-dual Lagrangians and Multiparameter Evolutions.- Direct Sum of Completely Self-dual Functionals.- Semilinear Evolution Equations with Self-dual Boundary Conditions.- Self-Dual Systems and their Antisymmetric Hamiltonians.- The Class of Antisymmetric Hamiltonians.- Variational Principles for Self-dual Functionals and First Applications.- The Role of the Co-Hamiltonian in Self-dual Variational Problems.- Direct Sum of Self-dual Functionals and Hamiltonian Systems.- Superposition of Interacting Self-dual Functionals.- Perturbations of Self-Dual Systems.- Hamiltonian Systems of Partial Differential Equations.- The Self-dual Palais-Smale Condition for Noncoercive Functionals.- Navier-Stokes and other Self-dual Nonlinear Evolutions.

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書名 Self-dual partial differential systems and their variational principles
著作者等 Ghoussoub, N.
Ghoussoub Nassif
シリーズ名 Springer monographs in mathematics
出版元 Springer
刊行年月 c2009
ページ数 xiv, 354 p.
大きさ 25 cm
ISBN 9780387848969
NCID BA88195961
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言語 英語
出版国 アメリカ合衆国