Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy

We study unbounded “supersolutions” of the evolutionary pp-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+np−0 or not summable to the power p−2p−2. There is a void gap between these exponents. Those summable to the power p−2p−2 induce a Radon measure, while those of the other kind do not. We also sketch similar results for the Porous Medium Equation.