6533b7d5fe1ef96bd12651a6

RESEARCH PRODUCT

Cheeger-harmonic functions in metric measure spaces revisited

Renjin JiangRenjin Jiang

subject

Pure mathematicsSemigroupta111Poincaré inequalityCurvatureLipschitz continuitySpace (mathematics)Measure (mathematics)symbols.namesakeHarmonic functionMetric (mathematics)symbolsAnalysisMathematics

description

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

yearjournalcountryeditionlanguage
2014-02-01Journal of Functional Analysis
10.1016/j.jfa.2013.11.022https://doi.org/10.1016/j.jfa.2013.11.022