Lipschitz regularity for viscosity solutions to parabolic \({\varvec{p(x,t)}}\)-Laplacian equations on Riemannian manifolds

  • Soojung KimEmail author


We study viscosity solutions to parabolic p(xt)-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.


\(p(x, t)\)-Laplacian operator Lipschitz regularity Viscosity solutions Riemannian manifold 

Mathematics Subject Classification

35K92 58J35 35D40 35B65 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsKorea Institute for Advanced StudySeoulRepublic of Korea

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