Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian |
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| Authors: | Goro Akagi Kazumasa Suzuki |
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| Institution: | (1) Media Network Center, Waseda University, 1-104 Totsuka-cho, Shinjuku-ku, Tokyo 169-8050, Japan;(2) Graduate School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan;(3) Present address: School of Systems Engineering, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama-shi, Saitama 337-8570, Japan;(4) Present address: Daiwa Institute of Research, 15-6 Fuyuki, Koto-ku, Tokyo 135-8460, Japan |
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| Abstract: | The existence, uniqueness and regularity of viscosity solutions to the Cauchy–Dirichlet problem are proved for a degenerate
nonlinear parabolic equation of the form  , where  denotes the so-called infinity-Laplacian given by  . 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 Cauchy–Dirichlet problem.
Dedicated to the memory of our friend Kyoji Takaichi.
The research of the first author was partially supported by Waseda University Grant for Special Research Projects, #2004A-366. |
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| Keywords: | 35K55 35K65 35D05 35D10 |
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