On a certain degenerate parabolic equation associated with the infinity-laplacian
Goro Akagi - Department of Machinery and Control Systems, College of Systems Engineering and Science,, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama-shi, Saitama 337-8570, Japan (email) Abstract: The comparison, uniqueness and existence of viscosity solutions to the Cauchy-Dirichlet problem are proved for a degenerate parabolic equation of the form $u_t$ = $\Delta_(\infty)u$, where $\Delta_(\infty)$ denotes the so-called infinity-Laplacian given by $\Delta_(\infty)u$ = $\Sigma^(N)_(i,j=1) u_x_i u_x_j u_(x_i)_x_j$ . Our proof relies on a coercive regularization of the equation, barrier function arguments and the stability of viscosity solutions.
Keywords: Degenerate parabolic equation, infinity-Laplacian, viscosity solution.
Received: September 2006; Revised: January 2007; Published: September 2007. |