Regularity of Supersolutions

TL;DR

This paper investigates the regularity properties of supersolutions to the Evolutionary p-Laplace Equation, establishing equivalences between different notions of supersolutions and demonstrating their Sobolev regularity.

Contribution

It proves the equivalence between viscosity supersolutions and p-supercaloric functions, and shows bounded viscosity supersolutions are weak supersolutions in a Sobolev space.

Findings

Viscosity supersolutions are equivalent to p-supercaloric functions.

Bounded viscosity supersolutions belong to a natural Sobolev space.

The paper clarifies the regularity and equivalence of supersolution concepts.

Abstract

The regularity for the supersolutions of the Evolutionary p-Laplace Equation is considered. In particular,the equivalence of viscosity supersolutions and p-supercaloric functions (lower semicontinuous supersolutions defined via a comparison principle) is considered. Bounded viscosity supersolutions are, in fact, weak supersolutions belonging to a natural Sobolev Space.