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 $$ 1< p_- \le p(x,t)\le p_+<\infty $$ 1 < p - ≤ p ( x , t ) ≤ p + < ∞ for some constants $$1<p_-\le p_+ <\infty $$ 1 < p - ≤ p + < ∞ . Using Ishii–Lions’ method, a Lipschitz estimate of viscosity solutions is established on Riemannian manifolds with sectional curvature bounded from below.
Nonlinear Differential Equations and Applications NoDEA – Springer Journals
Published: Jun 6, 2018
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