The infinity Laplacian, Aronsson’s equation and their generalizations
The infinity Laplacian, Aronsson’s equation and their generalizations
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DOI：
10.1090/s0002-9947-07-04338-3
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发表时间：
2008
影响因子：
1.3
通讯作者：
E. Barron;L. Evans;R. Jensen
中科院分区：
文献类型：
--
作者：
E. Barron;L. Evans;R. Jensen
无穷大拉普拉斯方程Δ ∞ u = 0最初是作为一类控制极小化泛函ess-sup U的L ∞变分问题的绝对极小值的Euler-Lagrange方程而产生的|杜|.更一般的泛函ess-sup U F（x，u，Du）类似地导出所谓的阿龙松方程AF [u] = 0。在本文中，我们表明，这些PDE运营商和各种有趣的推广也出现在其他几个方面似乎完全无关的L ∞变分问题，包括两个人的游戏理论与随机顺序的发挥，快速切换状态的控制问题，等等，由此产生的方程可以是抛物型和非齐次，方程类型排除在传统的L ∞变分问题。
The infinity Laplace equation Δ ∞ u = 0 arose originally as a sort of Euler-Lagrange equation governing the absolute minimizer for the L ∞ variational problem of minimizing the functional ess-sup U |Du|. The more general functional ess-sup U F(x, u, Du) leads similarly to the so-called Aronsson equation A F [u] = 0. In this paper we show that these PDE operators and various interesting generalizations also appear in several other contexts seemingly quite unrelated to L ∞ variational problems, including two-person game theory with random order of play, rapid switching of states in control problems, etc. The resulting equations can be parabolic and inhomogeneous, equation types precluded in conventional L ∞ variational problems.