Variational Methods for Boundary Value Problems For Systems of Elliptic Equations

Lavrent'ev, M.A.

ISBN 10: 0486450783 / ISBN 13: 9780486450780

Published by Mineola, New York, U.S.A.: Dover Pubns, 2006

About this Item

hardback in fine condition.

Seller Inventory # 128805

Bibliographic Details

• Title: Variational Methods for Boundary Value Problems For Systems of Elliptic Equations
• Publisher: Mineola, New York, U.S.A.: Dover Pubns
• Publication Date: 2006
• Language: English
• ISBN 10: 0486450783
• ISBN 13: 9780486450780
• Binding: Hardcover
• Condition: Fine
• Seller catalogs:
  • Mathematics

About this title

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.

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.