Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy. (January 2016) - Kinnunen, Juha; Lindqvist, Peter
Abstract: We study unbounded "supersolutions" of the evolutionary p -Laplace equation with slow diffusion. They are the same functions as the viscosity supersolutions. A fascinating dichotomy prevails: either they are locally summable to the power p − 1 + n p − 0 or not summable to the power p − 2 . There is a void gap between these exponents. Those summable to the power p − 2 induce a Radon measure, while those of the other kind do not. We also sketch similar results for the Porous Medium Equation.