# Modern Methods in the Calculus of Variations: $L^p$ Spaces

created by leoni on 18 Oct 2007
modified on 24 Oct 2007

[BibTeX]

Book

Inserted: 18 oct 2007
Last Updated: 24 oct 2007

Journal: Springer Monographs in Mathematics
Pages: 600
Year: 2007

Abstract:

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 semi-continuity 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 as a graduate textbook as well as a reference text for researchers in the field.

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