A Phragm\'en-Lindel\"of property of viscosity solutions to a class of nonlinear, possibly degenerate, parabolic equations

TL;DR

This paper investigates the Phragmén-Lindelöf property of viscosity solutions for a class of nonlinear, possibly degenerate, parabolic equations, providing theoretical insights and applications to doubly nonlinear equations.

Contribution

It establishes Phragmén-Lindelöf principles for viscosity solutions of doubly nonlinear parabolic equations, extending existing theory to degenerate cases.

Findings

Proved Phragmén-Lindelöf properties for a broad class of nonlinear parabolic equations.

Extended the theory to include degenerate and doubly nonlinear cases.

Provided applications demonstrating the practical relevance of the theoretical results.

Abstract

We study Phragm\'en-Lindel\"of properties of viscosity solutions to a class of doubly nonlinear parabolic equations in $\mathbb{R}^n\times (0,T)$. We also include an application to some doubly nonlinear equations.