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TITLE Lipschitz regularity for viscosity solutions to parabolic p(x,t)-Laplacian equations on Riemannian manifolds
KIAS AUTHORS Kim, Soojung
JOURNAL NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2018
ARCHIVE  
ABSTRACT We study viscosity solutions to parabolic p(x, t)-Laplacian equations on Riemannian manifolds under the assumption that a continuous exponent function p is Lipschitz continuous with respect to spatial variables, and satisfies 1 < p-= p(x, t) = p+ < 8 for some constants 1 < p-= p+ < 8. Using Ishii-Lions' method, a Lipschitz estimate of viscosity solutions is established on Riemannian manifolds with sectional curvature bounded from below.
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