Variational Problems with Concentration

By: Lina Martins

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Hardcover | 1 July 1999

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180 Pages

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24.13 x 17.15 x 1.27

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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.

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Introduction	p. 1
P-Capacity	p. 13
Generalized Sobolev Inequality	p. 18
Concentration Compactness Alternatives	p. 24
Compactness Criteria	p. 35
Entire Extremals	p. 44
Concentration and Limit Shape of Low Energy Extremals	p. 52
Robin Functions	p. 63
P-Capacity of Small Sets	p. 81
P-Harmonic Transplantation	p. 87
Concentration Points, Subconformal Case	p. 92
Conformal Low Energy Limits	p. 98
Applications	p. 109
Bernoulli's Free-boundary Problem	p. 119
Vortex Motion	p. 131
Bibliography	p. 151
Index	p. 161
Table of Contents provided by Blackwell. All Rights Reserved.

Variational Problems with Concentration

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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