On the viscosity solutions to Trudinger's equation

Abstract

We study the existence of positive viscosity solutions to Trudinger's equation for cylindrical domains $\Omega \times [0,T)$, where $\Omega \subset {\mathbb{R}}^n,n\ge 2,$ is a bounded domain, $T>0$ and $2\le p<\infty$. We show existence for general domains $\Omega ,$ when $n<p<\infty$. For $2\le p\le n$, we prove existence for domains $\Omega$ that satisfy a uniform outer ball condition. We achieve this by constructing suitable sub-solutions and super-solutions and applying Perron's method.

25 pages, 2 figures

References in corpus (1)

• On the viscosity solutions to a degenerate parabolic differential equation

Cited by in corpus (3)

• Asymptotics of viscosity solutions to some doubly nonlinear parabolic equations
• On the viscosity solutions to a class of nonlinear degenerate parabolic differential equations
• A Phragmén-Lindelöf property of viscosity solutions to a class of nonlinear, possibly degenerate, parabolic equations