Singular solutions for semi-linear parabolic equations on nonsmooth domains (Q2370720)

The author studies the existence of positive singular solutions for the semi-linear parabolic equation \[ \Delta_x u-{\partial \over \partial t} u+ \mu u^p=0\qquad \text{ on}\quad \Omega=D\times (0,\infty) \] where \(p>1,\) \(D\) is a bounded non-tangentially accessible domain in \({\mathbb R}^n,\) \(n\geq 2,\) and \(\mu \) 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.