Modern Methods in the Calculus of Variations

Irene Fonseca, Giovanni Leoni - Modern Methods in the Calculus of Variations: L^p spaces
Springer | ISBN 038735784X | Sept 2007 | 616 pages | PDF | 3.4 MB

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

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