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S-polar sets of super-brownian motions and solutions of nonlinear differential equations

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Abstract

This paper gives probabilistic expressions of the minimal and maximal positive solutions of the partial differential equation -1/2δv(x)+γ(x)v(x)α=0 in D, where D is a regular domain in ℝd(d⩾ 3) such that its complement D c is compact, γ(x) is a positive bounded integrable function in D, and 1 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Li Qiuyue & Ren Yanxia

Authors
  1. Li Qiuyue
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  2. Ren Yanxia
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Correspondence to Ren Yanxia.

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Qiuyue, L., Yanxia, R. S-polar sets of super-brownian motions and solutions of nonlinear differential equations. Sci. China Ser. A-Math. 48, 1683–1695 (2005). https://doi.org/10.1360/022005-009

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  • DOI: https://doi.org/10.1360/022005-009

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