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Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian

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Abstract

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

$u_t - \Delta _\infty ^N u = f$

, where Δ N∞ denotes the so-called normalized infinity Laplacian given by \(\Delta _\infty ^N u = \frac{1} {{|Du|^2 }}\left\langle {D^2 uDu,Du} \right\rangle \).

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Science, Nanjing University of Science & Technology, Nanjing, 210094, P. R. China

    Fang Liu & Xiao Ping Yang

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  1. Fang Liu
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  2. Xiao Ping Yang
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Correspondence to Fang Liu.

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

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Liu, F., Yang, X.P. Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian. Acta. Math. Sin.-English Ser. 31, 255–271 (2015). https://doi.org/10.1007/s10114-015-3244-6

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  • DOI: https://doi.org/10.1007/s10114-015-3244-6

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