Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations

TL;DR

This paper proves the equivalence of local and global parabolic BMO spaces, demonstrates exponential integrability of functions in these spaces, and establishes global integrability for supersolutions to doubly nonlinear parabolic equations.

Contribution

It extends classical BMO results to the parabolic setting and links these to the integrability of supersolutions in nonlinear parabolic equations.

Findings

Local and global parabolic BMO spaces are equal.

Functions in parabolic BMO are exponentially integrable.

Positive supersolutions have global integrability in a broad class of equations.

Abstract

We prove that local and global parabolic BMO spaces are equal thus extending the classical result of Reimann and Rychener. Moreover, we show that functions in parabolic BMO are exponentially integrable in a general class of space-time cylinders. As a corollary, we establish global integrability for positive supersolutions to a wide class of doubly nonlinear parabolic equations.