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

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Springer Science & Business Media, 22.08.2007 - 600 Seiten

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 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.

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.

 

Inhalt

II
3
III
22
IV
37
V
55
VI
77
VII
83
VIII
90
IX
103
XLIX
373
L
379
LI
380
LII
395
LIII
401
LV
404
LVI
413
LVII
428

X
113
XII
119
XIII
123
XIV
129
XV
139
XVI
148
XVII
156
XVIII
171
XIX
184
XX
190
XXII
198
XXIII
208
XXIV
218
XXV
229
XXVI
231
XXVII
245
XXVIII
247
XXIX
254
XXX
258
XXXI
262
XXXII
266
XXXIII
288
XXXIV
293
XXXV
300
XXXVI
318
XXXVII
322
XXXVIII
325
XXXIX
326
XL
331
XLII
334
XLIII
340
XLIV
350
XLV
354
XLVI
364
XLVII
365
XLVIII
369
LIX
435
LX
436
LXII
442
LXIII
445
LXIV
448
LXV
449
LXVI
464
LXVII
473
LXIX
478
LXX
485
LXXI
489
LXXII
491
LXXIV
492
LXXV
511
LXXVI
516
LXXVII
518
LXXVIII
532
LXXIX
533
LXXX
538
LXXXI
540
LXXXII
546
LXXXIII
547
LXXXIV
552
LXXXV
554
LXXXVI
558
LXXXVII
560
LXXXVIII
563
LXXXIX
566
XC
567
XCI
573
XCII
581
XCIII
584
XCIV
587
XCV
594
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