Degenerate homogeneous parabolic equations associated with the infinity-Laplacian

Details Degenerate homogeneous parabolic equations associated with the infinity-Laplacian Degenerate homogeneous parabolic equations associated with the infinity-Laplacian

2010-09-16

arxiv.org/abs/1009.3166v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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, $\Delta_\infty^h u = |Du|^{h-3} < D^2uDu,Du>$. 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.

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