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 \( 1< p_- \le p(x,t)\le p_+<\infty \) for some constants \(1<p_-\le p_+ <\infty \). 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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Kim, S. Lipschitz regularity for viscosity solutions to parabolic \({\varvec{p(x,t)}}\)-Laplacian equations on Riemannian manifolds. Nonlinear Differ. Equ. Appl. 25, 27 (2018). https://doi.org/10.1007/s00030-018-0519-5
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DOI: https://doi.org/10.1007/s00030-018-0519-5