TITLE

# Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian

AUTHOR(S)
Akagi, Goro; Suzuki, Kazumasa
PUB. DATE
April 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Apr2008, Vol. 31 Issue 4, p457
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The existence, uniqueness and regularity of viscosity solutions to the Cauchyâ€“Dirichlet problem are proved for a degenerate nonlinear parabolic equation of the form $$u_t = \Delta_\infty u$$ , where $$\Delta_\infty$$ denotes the so-called infinity-Laplacian given by $$\Delta_\infty u = \langle D^2 u Du, Du \rangle$$ . To do so, a coercive regularization of the equation is introduced and barrier function arguments are also employed to verify the equi-continuity of approximate solutions. Furthermore, the Cauchy problem is also studied by using the preceding results on the Cauchyâ€“Dirichlet problem.
ACCESSION #
28769631

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