Cheeger-harmonic functions in metric measure spaces revisited

By Renjin Jiang. 2013

68 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/33a44c567dbd488c0ad7ec33668a9f0627970b6f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Renjin Jiang
2. T. Coulhon
3. Adam S. Sikora
4. Pekka Koskela
5. Dachun Yang
6. Xuan Thinh Duong
7. Lixin Yan
8. P. Auscher

In Geometry and Topology

1. T. Coulhon
2. Pekka Koskela
3. Adam S. Sikora
4. Renjin Jiang
5. Andrés Navas
6. Jani Onninen
7. S. Hencl
8. M. Cristea

Citations in the corpus

• The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces (2014, methodology): “1] by choosing the natural Dirichlet energy onRCD∗(K,N) spaces and using the gradient estimates of harmonic functi ons from [27].”
• Gradient estimates for heat kernels and harmonic functions (2017, background): “In recent years, in a series of works [13, 52, 72, 73, 114, 115], Yau’s gradient estimate for harmonic functions and Li-Yau’s gradient estimate for heat kernels (and their local versions) have been further generalised to metric measure spaces and graphs satisfying suitable curvature assumptions; we ”