Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 266, Issue 3, Pages 1373-1394Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2013.11.022
Keywords
Cheeger-harmonic functions; Gradient estimate; Doubling measure; Poincare inequality; Curvature
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Funding
- National Natural Science Foundation of China [11301029]
- Fundamental Research Funds for Central Universities [2013YB60]
- Academy of Finland Grant [131477]
- Academy of Finland (AKA) [131477, 131477] Funding Source: Academy of Finland (AKA)
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Let (X, d, mu) be a complete metric measure space, with mu 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, mu). Gradient estimates for Cheeger-harmonic functions and solutions to a class of non-linear Poisson type equations are presented. (C) 2013 Elsevier Inc. All rights reserved.
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