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Abstract
The purpose of the paper is to describe the boundary behavior of the Green function of the parabolic equation Δu + Vu + 2((∇ϕ)/ϕ)·∇u - ut = 0 in D×ℝ+, where D is a bounded C1,1 domain in ℝn (n ≥ 3), ϕ is the positive eigenfunction corresponding to the first eigenvalue of -Δ, u0 is the initial value such that ϕu0 ∈ L2(D) and V belongs to a class of time dependent potentials which can be written as a nonlinear combination of derivatives of a function.
Keywords: Parabolic equation; Feynman–Kac formula; Jensen's inequality; boundary behavior; Green function
We would like to express our sincere thanks to the referees for their careful reading of the paper and for their helpful comments and suggestions.
Received: 2014-7-17
Revised: 2015-4-12
Accepted: 2015-5-9
Published Online: 2015-6-4
Published in Print: 2015-7-1
© 2015 by De Gruyter
