Degenerate homogeneous parabolic equations associated with the infinity-Laplacian

Abstract

We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem $u_t={\Delta }_{\infty }^{h}u$ where ${\Delta }_{\infty }^h$ is the $h$-homogeneous operator associated with the infinity-Laplacian, ${\Delta }_{\infty }^{h}u=|Du{|}^{h-3}<D^{2}uDu,Du>$. We also derive the asymptotic behavior of $u$ for the problem posed in the whole space and for the Dirichlet problem with zero boundary conditions.

21 pages

References in corpus (1)

• A porous medium equation involving the infinity-Laplacian. Viscosity solutions and asymptotic behaviour