A Phragm\'en-Lindel\"of property of viscosity solutions to a class of doubly nonlinear parabolic equations: Bounded Case

TL;DR

This paper investigates Phragmén-Lindelöf properties of viscosity solutions to certain nonlinear parabolic equations, establishing boundedness results and extending to doubly nonlinear cases with specific conditions on the operators involved.

Contribution

It introduces new Phragmén-Lindelöf principles for viscosity solutions of a class of doubly nonlinear parabolic equations under boundedness assumptions.

Findings

Established Phragmén-Lindelöf properties for viscosity solutions.

Derived results for positive solutions to doubly nonlinear equations.

Provided conditions on the operator H for boundedness.

Abstract

We study Phragm\'en-Lindel\"of properties for viscosity solutions to a class of nonlinear parabolic equations of the type $H(Du, D^2u+Z(u)Du\otimes Du)+\chi(t)|Du|^\sigma-u_t=0$ under a certain boundedness condition on $H$. We also state results for positive solutions to a class of doubly nonlinear equation $H(Du, D^2u)-f(u)u_t=0$.