This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in Lsubp 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.
This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in Lsubp 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.

Modern Methods in the Calculus of Variations: L^p Spaces
600
Modern Methods in the Calculus of Variations: L^p Spaces
600Product Details
ISBN-13: | 9780387357843 |
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Publisher: | Springer New York |
Publication date: | 09/12/2007 |
Series: | Springer Monographs in Mathematics |
Edition description: | 2007 |
Pages: | 600 |
Product dimensions: | 6.10(w) x 9.25(h) x 0.05(d) |