Parametrized Measures and Variational Principles

Lingua: inglese

Editore: Birkhäuser, Birkhäuser Mär 1997, 1997

3764356979 / 9783764356972

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This item is printed on demand - Print on Demand Titel. Neuware -Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under stand weak convergence and its behavior with respect to nonlinear functionals. Under suitable hypotheses, it yields a way of representing through integrals weak limits of compositions with nonlinear functions. It is particularly helpful in comprehending oscillatory phenomena and in keeping track of how oscilla tions change when a nonlinear functional is applied. Weak convergence also plays a fundamental role in the modern treatment of the calculus of variations, again because uniform bounds in norm for se quences allow to have weak convergent subsequences. In order to achieve the existence of minimizers for a particular functional, the property of weak lower semicontinuity should be established first. This is the crucial and most delicate step in the so-called direct method of the calculus of variations. A fairly large amount of work has been devoted to determine under what assumptions we can have this lower semicontinuity with respect to weak topologies for nonlin ear functionals in the form of integrals. The conclusion of all this work is that some type of convexity, understood in a broader sense, is usually involved.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 228 pp. Englisch. …

Codice articolo 9783764356972

Titolo
Parametrized Measures and Variational Principles
Autore
Pablo Pedregal
Editore
Birkhäuser, Birkhäuser Mär 1997
Anno di pubblicazione
1997
Condizione
Neu
Rilegatura
Buch
Lingua
inglese
ISBN 10
3764356979
ISBN 13
9783764356972
Peso dell'articolo
512 grammi
Dimensioni
241x160x17 mm

buchversandmimpf2000

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