Summability of semicontinuous supersolutions to a quasilinear parabolic equation

Abstract

We study the so-called p-superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when p = 2, we have supercaloric functions and the heat equation. We show that the p-superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given. Mathematics Subject Classification (2000): 35K55.