Variational problems with concentration /

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Bibliographic Details
Author / Creator:Flucher, Martin, 1962-
Imprint:Boston : Birkhauser, 1999.
Description:p. cm.
Language:English
Series:Progress in nonlinear differential equations and their applications v. 36
Subject:
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/3960699
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ISBN:3764361360 (alk. paper)
0817661360 (alk. paper)
Notes:Includes bibliographical references and index.
Description
Summary:To start with we describe two applications of the theory to be developed in this monograph: Bernoulli's free-boundary problem and the plasma problem. Bernoulli's free-boundary problem This problem arises in electrostatics, fluid dynamics, optimal insulation, and electro chemistry. In electrostatic terms the task is to design an annular con­ denser consisting of a prescribed conducting surface 80. and an unknown conduc­ tor A such that the electric field 'Vu is constant in magnitude on the surface 8A of the second conductor (Figure 1.1). This leads to the following free-boundary problem for the electric potential u. -~u 0 in 0. \A, u 0 on 80., u 1 on 8A, 8u Q on 8A. 811 The unknowns are the free boundary 8A and the potential u. In optimal in­ sulation problems the domain 0. \ A represents the insulation layer. Given the exterior boundary 80. the problem is to design an insulating layer 0. \ A of given volume which minimizes the heat or current leakage from A to the environment ]R.n \ n. The heat leakage per unit time is the capacity of the set A with respect to n. Thus we seek to minimize the capacity among all sets A c 0. of equal volume.
Physical Description:p. cm.
Bibliography:Includes bibliographical references and index.
ISBN:3764361360
0817661360