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Название: Introduction to the Calculus of Variations
Автор: Dacorogna B.
The calculus of variations is a classical subject, but is very much alive and evolving, thanks to its links to other branches of mathematics such as geometry and differential equations and its applications to physics, engineering, economics and biology. Decorogna (Federal Polytechnic School, Switzerland) writes for the non-specialist who wants a thorough background in the subject. Topics include a review of preliminaries such as continuous and Holder continuous functions, Sobolev spaces and convex analysis; classical methods such as Euler-Lagrange equations; direct methods such as the Dirichlet integral; regularity, such as the one-dimensinal case; minimal surfaces such as in the Douglas- Courant-Tonelli method; and isoperimetric inequality. Decorogna includes over 70 exercises (and solutions) and a well-done bibliography. This is an English translation of Introduction au calcul des variations published by Presses Polytechniques et Universitaires Romandes in 1992. Distributed by World Scientific