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Self-dual Partial Different...
Based on recent research by the author and his graduate students, this text describes novel variational formulations and resolutions of a large class of partial differential equations and evolutions, many of which are not amenable to the methods of the classical calculus of variations. While it contains many new results, the general and unifying framework of the approach, its versatility in solving a disparate set of equations, and its reliance on basic functional analytic principles, makes it suitable for an intermediate level graduate course. 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. It is the author's hope that this material will become standard for all graduate students interested in convexity methods for PDEs. Nassif Ghoussoub is a Distinguished University Professor at the University of British Columbia. He was editor-in-chief of the Canadian Journal of Mathematics for the period 1993-2003, and has served on the editorial board of various international journals. He is the founding director of the Pacific Institute for the Mathematical Sciences (PIMS), and a co-founder of the MITACS Network of Centres of Excellence. He is also the founder and scientific director of the Banff International Research Station (BIRS). He is the recipient of many awards, including the Coxeter-James, and the Jeffrey-Williams prizes. He was elected Fellow of the Royal Society of Canada in 1993, and was the recipient of a Doctorat Honoris Causa from the Universite Paris-Dauphine in 2004
Monografía
monografia Rebiun13410005 https://catalogo.rebiun.org/rebiun/record/Rebiun13410005 cr nn 008mamaa 100301s2009 xxu| s |||| 0|eng d 9780387848976 10.1007/978-0-387-84897-6 doi UPVA 996887898603706 UAM 991007632779304211 CUNEF 991000429254808131 CBUC 991004876577406711 PBKF bicssc MAT037000 bisacsh 515.7 23 Ghoussoub, Nassif Self-dual Partial Differential Systems and Their Variational Principles Recurso electrónico-En línea] by Nassif Ghoussoub New York, NY Springer New York 2009 New York, NY New York, NY Springer New York digital Springer Monographs in Mathematics 1439-7382 Mathematics and Statistics (Springer-11649) Preface -- Introduction -- 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 -- 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 with Self-dual Boundary Conditions -- 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 -- Hamiltonian Systems of Partial Differential Equations -- The Self-dual Palais-Smale Condition for Noncoercive Functionals -- Navier-Stokes and other Self-dual Nonlinear Evolutions -- References Accesible sólo para usuarios de la UPV Recurso a texto completo Based on recent research by the author and his graduate students, this text describes novel variational formulations and resolutions of a large class of partial differential equations and evolutions, many of which are not amenable to the methods of the classical calculus of variations. While it contains many new results, the general and unifying framework of the approach, its versatility in solving a disparate set of equations, and its reliance on basic functional analytic principles, makes it suitable for an intermediate level graduate course. 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. It is the author's hope that this material will become standard for all graduate students interested in convexity methods for PDEs. Nassif Ghoussoub is a Distinguished University Professor at the University of British Columbia. He was editor-in-chief of the Canadian Journal of Mathematics for the period 1993-2003, and has served on the editorial board of various international journals. He is the founding director of the Pacific Institute for the Mathematical Sciences (PIMS), and a co-founder of the MITACS Network of Centres of Excellence. He is also the founder and scientific director of the Banff International Research Station (BIRS). He is the recipient of many awards, including the Coxeter-James, and the Jeffrey-Williams prizes. He was elected Fellow of the Royal Society of Canada in 1993, and was the recipient of a Doctorat Honoris Causa from the Universite Paris-Dauphine in 2004 Reproducción electrónica Forma de acceso: Web Mathematics Functional analysis Differential equations, partial Mathematics Functional Analysis Partial Differential Equations SpringerLink (Servicio en línea) Springer eBooks Springer eBooks Printed edition 9780387848969 Springer Monographs in Mathematics 1439-7382