A convexity principle for interacting gases
A convexity principle for interacting gases
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DOI：
10.1006/aima.1997.1634
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发表时间：
1997-06-01
影响因子：
1.7
通讯作者：
McCann, RJ
中科院分区：
文献类型：
--
作者：
McCann, RJ
基于R-d上Borel概率度量之间的一种新颖而自然的内插，引入了一组新的不等式。利用这些估计代替凸性或重排不等式，解决了一类吸引气体模型的存在性和唯一性问题。在这些模型中，气体通过一种随距离增加的力与自身相互作用，并受压力与密度相关的状态方程P=P(Rho)的支配。对于一维气体，假定P(Rho)/Rho((d-1)/d)不减小。通过证明系统的内能和势能是插值参数的凸函数，证明了能量最小化状态的存在--直到平移都是唯一的。Rho(T)(-p/d)作为t的函数建立的凹性是[0，1]的一个元素，将Brunn-Minkowski不等式从集合推广到测度。(C)1997年学术出版社。
A new set of inequalities is introduced, based on a novel but natural interpolation between Borel probability measures on R-d. Using these estimates in lieu of convexity or rearrangement inequalities, the existence and uniqueness problems are solved for a family of attracting gas models. In these models, the gas interacts with itself through a force which increases with distance and is governed by an equation of state P = P(rho) relating pressure to density. P(rho)/rho((d-1)/d) is assumed non-decreasing for a ti-dimensional gas. By showing that the internal and potential energies for the system are convex Functions of the interpolation parameter, an energy minimizing state - unique up to translation - is proven to exist. The concavity established for \\rho(t)\\(-p/d) as a function of t is an element of [0, 1] generalizes the Brunn-Minkowski inequality from sets to measures. (C) 1997 Academic Press.