The comparison, uniqueness and existence of viscosity solutions to the Cauchy-Dirichlet problem are proved for a degenerate parabolic equation of the form ut = Δ∞u, where Δ∞ denotes the so-called infinity-Laplacian given by Δ∞u = ΣNi,j=1 uxiuxj u xixj. Our proof relies on a coercive regularization of the equation, barrier function arguments and the stability of viscosity solutions.
|Number of pages||10|
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - 2007 Sept|
- Degenerate parabolic equation
- Viscosity solution