Free boundaries in optimal transport and Monge-Ampère obstacle problems
نویسندگان
چکیده
منابع مشابه
Free boundaries in optimal transport and Monge-Ampère obstacle problems
Given compactly supported 0 ≤ f, g ∈ L1(R), the problem of transporting a fraction m ≤ min{‖f‖L1 , ‖g‖L1} of the mass of f onto g as cheaply as possible is considered, where cost per unit mass transported is given by a cost function c, typically quadratic c(x,y) = |x − y|/2. This question is shown to be equivalent to a double obstacle problem for the Monge-Ampère equation, for which sufficient ...
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Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries uses methods from PDEs, Calculus of Variations, Geometric Measure Theory, and Harmonic Analysis. The most important mathematical challenge in this context is ...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2010
ISSN: 0003-486X
DOI: 10.4007/annals.2010.171.673