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

Lipschitz regularity for viscosity solutions to parabolic $${\varvec{p(x,t)}}$$ p ( x , t )... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

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

, Volume 25 (4) – Jun 6, 2018
32 pages

/lp/springer_journal/lipschitz-regularity-for-viscosity-solutions-to-parabolic-varvec-p-x-t-0GbFDqnHZh
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
D.O.I.
10.1007/s00030-018-0519-5
Publisher site
See Article on Publisher Site

### 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 $$1< p_- \le p(x,t)\le p_+<\infty$$ 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.

### Journal

Nonlinear Differential Equations and Applications NoDEASpringer Journals

Published: Jun 6, 2018

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