Martin boundaries of elliptic skew products, semismall perturbations, and fundamental solutions of parabolic equations

摘要

We consider positive solutions of elliptic partial differential equations on noncompact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations. (C) 2002 Elsevier Science (USA). [References: 97]