Viscosity Solutions to a Parabolic Inhomogeneous Equation Associated with Infinity Laplacian

Viscosity Solutions to a Parabolic Inhomogeneous Equation Associated with Infinity Laplacian

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摘要 We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut-△ ∞N u=f, where An denotes the so-called normalized infinity Laplacian given by △∞ Nu=1/｜Du｜2〈D2uDu,Du〉. We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut-△ ∞N u=f, where An denotes the so-called normalized infinity Laplacian given by △∞ Nu=1/｜Du｜2〈D2uDu,Du〉.

作者 Fang LIU Xiao Ping YANG

机构地区 Department of Applied Mathematics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第2期255-271,共17页 数学学报（英文版）

基金 Supported by National Natural Science Foundation of China(Grant Nos.11071119 and 11171153)

关键词 Parabolic equation infinity Laplacian viscosity solution inhomogeneous equation comparison principle EXISTENCE Parabolic equation, infinity Laplacian, viscosity solution, inhomogeneous equation, comparison principle, existence

分类号 O175 [理学—基础数学]

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Acta Mathematica Sinica,English Series

2015年第2期

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Viscosity Solutions to a Parabolic Inhomogeneous Equation Associated with Infinity Laplacian

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