{"product_id":"variational-problems-with-concentration-von-martin-f-bach","title":"Variational Problems with Concentration","description":"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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783034897297\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783764361365\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783034897297","offer_id":49592344346949,"sku":"9783034897297","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783764361365","offer_id":49593035391301,"sku":"9783764361365","price":117.69,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/7ce6b079-9ce0-408a-a931-96b633fdc756.jpg?v=1772173905","url":"https:\/\/shop.autorenwelt.de\/en\/products\/variational-problems-with-concentration-von-martin-f-bach","provider":"Autorenwelt Shop","version":"1.0","type":"link"}