Variational Methods for Boundary Value Problems for Systems of Elliptic Equations (Dover Books on Mathematics)

Book Details:

• Book Title: Variational Methods in the Theory of Boundary Value Problems

• Author: M. A. Lavrent’ev

• Binding: Paperback

• ISBN: 9780486661704

• Pages: 160

• Release Date: 14-01-2016

• Language: English

About the Book:

In this classic monograph, distinguished mathematician M. A. Lavrent’ev introduces an innovative approach to classical boundary value problems that combines geometric properties of conformal and quasi-conformal mappings. This method is designed to be accessible not only to mathematicians but also to theoreticians in mechanics.

The book presents the general basic scheme for solving variational problems, first proposed by Hilbert and later developed by Tonnelli. The initial chapters focus on variational principles in the theory of conformal mapping and the behavior of conformal transformations on the boundary. Further chapters delve into hydrodynamic applications, quasiconformal mappings, and the simplest classes of non-linear systems.

Mathematicians will find particular interest in the proofs of existence and uniqueness theorems, as well as the development of quasi-conformal mappings. The book also includes approximate formulas for conformal and quasi-conformal transformations, which will be of particular value to theoreticians in mechanics.

Key Features:

• Innovative approach to boundary value problems.

• Focus on conformal and quasi-conformal mappings.

• Applications to hydrodynamics and non-linear systems.

• Includes existence and uniqueness theorems.

• Valuable for both mathematicians and mechanical theorists.