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   作者單位： LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China  刊 名： 中國科學A輯（英文版）  SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS)  年，卷(期)： 2005 48(12)  分類號： O1  關鍵詞： super-Brownian motion   nonlinear differential equation   minimal positive solutions   maximal positive solutions   S-polar sets