Singular solutions for semi-linear parabolic equations on nonsmooth domains

We prove the existence of positive singular solutions for the semi-linear parabolic equation Δxu− ∂ ∂t u+ μup = 0 on Ω = D×]0,∞[, wherep >1,D is a bounded NTA-domain in Rn, n 2, and μ is in a general class of signed Radon measures on D covering the elliptic Kato class of potentials adopted by Zhang and Zhao. A new proof of the result based on a simple fixed point theorem is also given. © 2006 Elsevier Inc. All rights reserved.