Variational Methods for Boundary Value Problems: for Systems of Elliptic Equations (Dover Phoenix Edition)
M. A. Lavrentev
ISBN 10: 0486450783 ISBN 13: 9780486450780
Published by Dover Publications, 2012
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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.
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.
About the Author: M. A. Lavrent'ev (1900–80) was a prominent Soviet mathematician, associated with Moscow State University and the Steklov Institute of Mathematics.
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Bibliographic Details
Title: Variational Methods for Boundary Value ...
Publisher: Dover Publications
Publication Date: 2012
Binding: Hardcover
Condition: Good
Dust Jacket Condition: No Jacket
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Variational Methods for Boundary Value Problems For Systems of Elliptic Equations
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ISBN 10: 0486450783
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Variational Methods for Boundary Value Problems For Systems of Elliptic Equations
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Mineola, New York, U.S.A.: Dover Pubns, 2006
ISBN 10: 0486450783
ISBN 13: 9780486450780
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