Cheeger-harmonic functions in metric measure spaces revisited

Abstract

Let $(X,d,\mu )$ be a complete metric measure space, with $\mu$ a locally doubling measure, that supports a local weak $L^2$-Poincaré inequality. By assuming a heat semigroup type curvature condition, we prove that Cheeger-harmonic functions are Lipschitz continuous on $(X,d,\mu )$. Gradient estimates for Cheeger-harmonic functions and solutions to a class of non-linear Poisson type equations are presented.

Proof of Proposition 3.1 is modified, Proposition 3.4 of [20] is not needed in the proof anymore. Comments are welcome

References in corpus (2)

• Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
• A Note on Lipschitz Continuity of Solutions of Poisson Equations in Metric Measure Spaces

Cited by in corpus (2)

• A Note on Lipschitz Continuity of Solutions of Poisson Equations in Metric Measure Spaces
• The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces