Regularity of viscosity solutions of a degenerate parabolic equation

Lu, Yun-Guang; Qian, Liwen

doi:10.1090/S0002-9939-01-06313-4

Regularity of viscosity solutions of a degenerate parabolic equation
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by Yun-Guang Lu and Liwen Qian PDF

Proc. Amer. Math. Soc. 130 (2002), 999-1004 Request permission

Abstract:

We study the Cauchy problem for the nonlinear degenerate parabolic equation of second order \[ \left \{ \begin {array}{l} u_t=u\triangle u-\gamma |\nabla u|^2 \ \ \text {in} \hspace {0.3cm} \Omega =R^N \times R^{+}, u(x,0)=u_{0}(x)\ \ \ \ \ \ \ \ \text {in} \hspace {0.3cm} R^{N}, \end {array} \right . \] and present regularity results for the viscosity solutions.

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