On a certain degenerate parabolic equation associated with the infinity-Laplacian

Goro Akagi; Kazumasa Suzuki

On a certain degenerate parabolic equation associated with the infinity-Laplacian

Goro Akagi, Kazumasa Suzuki

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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 = Δ_∞u, where Δ_∞ denotes the so-called infinity-Laplacian given by Δ_∞u = Σ^N_i,j=1 u_xiu_xj u _xixj. Our proof relies on a coercive regularization of the equation, barrier function arguments and the stability of viscosity solutions.

Original language	English
Pages (from-to)	18-27
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems
Issue number	SUPPL.
Publication status	Published - 2007 Sept

Keywords

Degenerate parabolic equation
Infinity-Laplacian
Viscosity solution

Cite this

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title = "On a certain degenerate parabolic equation associated with the infinity-Laplacian",

abstract = "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.",

keywords = "Degenerate parabolic equation, Infinity-Laplacian, Viscosity solution",

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TY - JOUR

T1 - On a certain degenerate parabolic equation associated with the infinity-Laplacian

AU - Akagi, Goro

AU - Suzuki, Kazumasa

PY - 2007/9

Y1 - 2007/9

N2 - 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.

AB - 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.

KW - Degenerate parabolic equation

KW - Infinity-Laplacian

KW - Viscosity solution

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AN - SCOPUS:84878059703

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JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - SUPPL.

ER -

On a certain degenerate parabolic equation associated with the infinity-Laplacian

Abstract

Keywords

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