Nonlinear Parabolic Capacity and Polar Sets of Superparabolic Functions

We extend the theory of the thermal capacity for the heat equation to nonlinear parabolic equations of the p-Laplacian type. We study definitions and properties of the nonlinear parabolic capacity and show that the capacity of a compact set can be represented via a capacitary potential. As an application, we show that polar sets of superparabolic functions are of zero capacity. The main technical tools used include estimates for equations with measure data and obstacle problems.