Variational Problems with Concentration

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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Product details

• Authors: Martin F Bach, Martin F. Bach, Lina Martins, Martin Flucher, Martin Bach
• Publisher: Birkhäuser
• Content: Book
• Product form: Hardback
• Publication date: 01.01.1999
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis
• EAN: 9783764361365
• ISBN: 978-3-7643-6136-5
• Weight (packing): 435 g
• Series: Progress in Nonlinear Differential Equations and Their Applications > Vol.36; Progress in Nonlinear Differential Equations and Their Applications > 36
• Subjects: extrema, compactness, differentialequation, numericalmethods, partialdifferentialequation, variationalcalculus, Euler-Lagrangeequation, Robinfunctions