Singular solutions for semi-linear parabolic equations on nonsmooth domains

AbstractWe prove the existence of positive singular solutions for the semi-linear parabolic equation Δxu−∂∂tu+μup=0 on Ω=D×]0,∞[, where p>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