Uniform energy distribution for an isoperimetric problem with long-range interactions
نویسندگان
چکیده
منابع مشابه
Uniform Energy Distribution for an Isoperimetric Problem with Long-range Interactions
S(u) denotes the interfacial area associated with the surfaces upon which u jumps, and G(x, y) denotes the Green’s function for − on QL with Neumann boundary conditions. The variational problem consists of competing short-range (S(u)) and long-range (the nonlocal Green’s function term) contributions. The former term is attractive, favoring large domains of pure phases with boundaries of minimal...
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We study minimizers of a nonlocal variational problem. The problem is a mathematical paradigm for the ubiquitous phenomenon of energy-driven pattern formation induced by competing short and long-range interactions. The short range interaction is attractive and comes from an interfacial energy, the long range interaction is repulsive and comes from a nonlocal energy contribution. In particular, ...
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Questions about geometrical configurations which lead to extremal value of a spectral quantity represent a classical topic in mathematical physics; recall the Faber-Krahn inequality [Fa, Kr], the PPW-conjecture proved by Ashbaugh and Benguria [AB], and numerous other examples. A particular place in this list is occupied by the Dirichlet problem for the Laplacian in annular strips and their high...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2008
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-08-00622-x