S-polar sets of super-Brownian motions and solutions of nonlinear differential equations
This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.
作 者： LI Qiuyue REN Yanxia 作者单位： LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China 刊 名： 中国科学A辑（英文版） SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS) 年，卷(期)： 2005 48(12) 分类号： O1 关键词： super-Brownian motion nonlinear differential equation minimal positive solutions maximal positive solutions S-polar sets