Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces☆
By Pekka Koskela, Kai Rajala, Nageswari Shanmugalingam. 2003
69 citations recorded by the source corpus.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/0bde96788134b7ddbf034ebe0e56ea3062e3d799
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
Citations in the corpus
- Cheeger-harmonic functions in metric measure spaces revisited (2013, methodology): “itz continuity of Cheegerharmonic functions. Later, a quantitative gradient estimate for Cheeger-harmonic functions was given in [16]. The main aim of this paper is to relax the Ahlfors regularity in [20, 16] to doubling of the measure. Besides this, gradient estimates for a class of non-linear Pois”
- Space of Ricci Flows I (2009, background): “excellent properties of heat kernels, from Proposition 2.11 to Proposition 2.13, we are ready to generalize the celebrated Cheng-Yau estimate (c.f. [36]) to our setting. We basically follow the paper [58]. However, due to the essential importance of this estimate and the excellent geometry of our un”
- The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces (2014, methodology): “ the Ricci curvature and is a powerful tool in geometric analysis, where Γ is the carre´ du champ operator and Ht is the corresponding heat flow; see [9, 10]. On metric measure spaces, it was shown in [30, 27] that a locally doubling measure, a local weak L2- Poincare´ inequality and a Bakry-Emery ty”
- Yau's gradient estimates on Alexandrov spaces (2010, background): “etailed exposition of Petrunin’s proof is contained in Proposition 5.3 below. Furthermore, we will prove the Lipschitz continuity of solutions of general Poisson equation, see Corollary 5.5 below. In [21], Koskela–Rajala– Shanmugalingam proved that the same regularity of Cheeger-harmonic functions o”