Deals with semilinear Dirichlet problems and similar equations involving the p-Laplacian. This work offers a detailed analysis of low-energy solutions. It analyzes the asymptotic behaviour of low-energy solutions in the vicinity of the concentration point on a microscopic scale. Series: Progress in Nonlinear Differential Equations and Their Applications. Num Pages: 171 pages, biography. BIC Classification: PBKJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 235 x 155 x 11. Weight in Grams: 432. . 1999. Hardback. . . . . Books ship from the US and Ireland.

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Bibliographic Details

Title: Variational Problems with Concentration
Publisher: Birkhauser Verlag AG
Publication Date: 1999
Language: English
ISBN 10: 3764361360
ISBN 13: 9783764361365
Binding: Hardcover
Condition: New

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Synopsis

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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"This material is very rich, because various alternatives are possible. The book provides a good systematic overview of this difficult topic."

--Zentralblatt Math

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