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Titlebook: Variational Problems with Concentration; Martin Flucher Book 1999 Springer Basel AG 1999 Euler–Lagrange equation.Robin functions.Variation

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發(fā)表于 2025-3-21 18:14:14 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Variational Problems with Concentration
編輯Martin Flucher
視頻videohttp://file.papertrans.cn/981/980615/980615.mp4
叢書名稱Progress in Nonlinear Differential Equations and Their Applications
圖書封面Titlebook: Variational Problems with Concentration;  Martin Flucher Book 1999 Springer Basel AG 1999 Euler–Lagrange equation.Robin functions.Variation
描述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.
出版日期Book 1999
關鍵詞Euler–Lagrange equation; Robin functions; Variational calculus; compactness; differential equation; extre
版次1
doihttps://doi.org/10.1007/978-3-0348-8687-1
isbn_softcover978-3-0348-9729-7
isbn_ebook978-3-0348-8687-1Series ISSN 1421-1750 Series E-ISSN 2374-0280
issn_series 1421-1750
copyrightSpringer Basel AG 1999
The information of publication is updating

書目名稱Variational Problems with Concentration影響因子(影響力)




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沙發(fā)
發(fā)表于 2025-3-21 22:51:50 | 只看該作者
Vortex Motion in Two Dimensional Hydrodynamics,reen’s function. As an application of the properties of the Robin function derived in the previous chapters we prove long time existence of vortex pairs. This result is optimal, since three vortices can collide in finite time. We report from our work with B. Gustafsson [52].
板凳
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地板
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5#
發(fā)表于 2025-3-22 09:43:04 | 只看該作者
Concentration and Limit Shape of Low Energy Extremals, corresponding semilinear results have been obtained with S. Müller [55]. In the smooth case additional information can be derived from the Euler Lagrange equation. For the supremum in the variational problem (1.2) we use the following abbreviation.
6#
發(fā)表于 2025-3-22 14:50:59 | 只看該作者
P-Harmonic Transplantation,s the conformai transplantation. Each of them is a powerful tool for the construction of comparison functions. They are complementary to symmetrization in the sense that they provide lower bounds when symmetrization gives upper bounds and vice versa. In contrast to symmetrization they take the geome
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發(fā)表于 2025-3-22 21:02:36 | 只看該作者
,Bernoulli’s Free-boundary Problem,statics, and further applications. In the . a connected domain Ω in ?. and a constant . > 0 are given. The task is to find a subset .?Ω and a potential .: Ω. → ? such that .(see Figure 1.1 on page 2). In the . ?. is exterior to ?Ω with . = 1 on ?Ω, . = 0 on ?A and . < 0 (Figure 14.1). The same probl
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發(fā)表于 2025-3-23 00:09:09 | 只看該作者
Vortex Motion in Two Dimensional Hydrodynamics,action of point vortices with the walls of the container is governed by the Robin function, while the interaction of vortex pairs is governed by the Green’s function. As an application of the properties of the Robin function derived in the previous chapters we prove long time existence of vortex pai
9#
發(fā)表于 2025-3-23 03:39:21 | 只看該作者
Book 1999Bernoulli‘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 electri
10#
發(fā)表于 2025-3-23 05:39:46 | 只看該作者
ularly Victorian work, one marked by the era’s spiritual crisis, a crisis that was brought to a head by the 1859 publication of Charles Darwin’s ... Yet, after its 1863 publication, . was apparently popular up through the 1920s. The story provided inspiration for beautiful illustrations by Linley Sa
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