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Modern Methods in the Calcu...
This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in Lp spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science
Monografía
monografia Rebiun17223252 https://catalogo.rebiun.org/rebiun/record/Rebiun17223252 cr nn 008mamaa 100301s2007 xxu| s |||| 0|eng d 9780387690063 10.1007/978-0-387-69006-3 doi UR0288867 UIB (369864) UAM 991007838443104211 UPVA 996880194203706 CUNEF 991000429550808131 CBUC 991004876766106711 CBUC 991003518407606714 CBUC 991000995638706718 CBUC 991004008243206713 CBUC 991000727553506712 CBUC 991010402730206709 CBUC 991015710709706706 CBUC 991010848019706708 PBKQ bicssc PBU bicssc MAT005000 bisacsh MAT029020 bisacsh Fonseca, Irene Modern Methods in the Calculus of Variations: Lp Spaces Recurso electrnico] by Irene Fonseca, Giovanni Leoni New York, NY Springer New York 2007 New York, NY New York, NY Springer New York digital Springer Monographs in Mathematics 1439-7382 Preface -- Measure Theory and Lp Spaces -- Measures -- Lp spaces -- The Direct method and lower semicontinuity -- Convex analysis -- Functionals defined on Lp -- Integrands f = f (z) -- Integrands f = f (x; z) -- Integrands f = f (x; u; z) -- Young measures -- A Appendix -- B Notes and open problems -- C Notation and List of symbols -- Index. Acceso restringido a miembros de la UGR This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in Lp spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science Mathematics Global analysis (Mathematics) Differential equations, partial Mathematical optimization Materials Mathematics Calculus of Variations and Optimal Control; Optimization Continuum Mechanics and Mechanics of Materials Analysis Partial Differential Equations Applications of Mathematics Leoni, Giovanni SpringerLink (Online service) SpringerLink ebooks (Servicio en lnea) Springer eBooks Springer eBooks Printed edition 9780387357843 Springer Monographs in Mathematics 1439-7382