Variational methods
Subtitle: applications to nonlinear partial differential equations and Hamiltonian systems
By: Michael Struwe.
Edition: 4th ed.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete -- 3. Folge, v. 34 = -- A series of modern surveys in mathematics
Publisher: Springer
Published: 2008
Place of publication: Berlin
Language: ger
Number of pages: 302
ISBN-13: 9783540740124; 9783540740131
Subjects: Calculus of variations; Differential equations, Nonlinear; Hamiltonian systems
Description: Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Also the recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. Aside from these more significant additions, a number of smaller changes throughout the text have been made and the references have been updated.
Notes: Includes bibliographical references (p. [277]-300) and index.