Variational Methods for Boundary Value Problems For Systems of Elliptic Equations

Published by Mineola, New York, U.S.A.: Dover Pubns, 2006
ISBN 10: 0486450783 / ISBN 13: 9780486450780
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Synopsis: In this famous work, a distinguished Russian mathematical scholar presents an innovative approach to classical boundary value problems ? one that may be used by mathematicians as well as by theoreticians in mechanics. The approach is based on a number of geometric properties of conformal and quasi-conformal mappings. It employs the general basic scheme for the solution of variational problems first suggested by Hilbert and developed by Tonnelli. The method lies on the boundary between the classical methods of analysis, with their concrete estimates and approximate formulae, and the methods of the theory of functions of a real variable with their special character and general theoretical quantitative aspects.
The first two chapters cover variational principles of the theory of conformal mapping and behavior of a conformal transformation on the boundary. Succeeding chapters address hydrodynamic applications and quasi-conformal mappings, as well as linear systems and the simplest classes of non-linear systems.
Mathematicians will find the method of the proof of the existence and uniqueness theorem of special interest. Theoreticians in mechanics will consider the approximate formulae for conformal and quasi-conformal mappings highly useful in solving many concrete problems of the mechanics of continuous media. This classic work is also a valuable resource for researchers in the fields of mathematics and physics.

Product Description: In this work, a distinguished Russian mathematical scholar presents an innovative approach to classical boundary value problems. The first two chapters cover variational principles of the theory of conformal mapping and behavior of a conformal transformation on the boundary. Succeeding chapters address hydrodynamic applications, quasi-conformal mappings, linear systems and the simplest classes of non-linear systems.

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Title: Variational Methods for Boundary Value ...
Publisher: Mineola, New York, U.S.A.: Dover Pubns
Publication Date: 2006
Binding: Hardcover
Book Condition: New

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