Variational Methods in Mathematical Physics: A Unified Approach (Theoretical and Mathematical Physics) - Softcover

Blanchard, Philippe; Brüning, Erwin

Softcover

ISBN 10: 3642827004 ISBN 13: 9783642827006

Verlag: Springer, 2011

Inhaltsangabe

This is a nicely organized introduction to the direct methods of variational calculus focusing on the study of critical points of nonlinear functionals. It addresses students of mathematics and physics, and gives many applications to mechanics, classical field theory, boundary and eigenvalue problems of important partial differential equations, and also modern Thomas-Fermi theory.

Über diesen Titel

Reseña del editor

The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal­ culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).

Reseña del editor

This textbook is a comprehensive introduction to variational methods. Its unifying aspect, based on appropriate concepts of compactness, is the study of critical points of functionals via direct methods. It shows the interactions between linear and nonlinear functional analysis. Addressing in particular the interests of physicists, the authors treat in detail the variational problems of mechanics and classical field theories, writing on local linear and nonlinear boundary and eigenvalue problems of important classes of nonlinear partial differential equations, and giving more recent results on Thomas-Fermi theory and on problems involving critical nonlinearities. This book is an excellentintroduction for students in mathematics and mathematical physics.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 3642827004
• ISBN 13: 9783642827006
• Einband: Tapa blanda
• Anzahl der Seiten: 424
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland