Weak reverse Hölder inequality of weakly A-harmonic sensors and Hölder continuity of A-harmonic sensors

Weighted Caccioppoli-type Estimates and Weak Reverse Hölder Inequalities for A-harmonic Tensors

We obtain a local weighted Caccioppoli-type estimate and prove the weighted version of the weak reverse Hölder inequality for A-harmonic tensors.

The Reverse Hölder Inequality for the Solution to p-Harmonic Type System

Recently, amount of work about the A-harmonic equation for the differential forms has been done. In fact, the A-harmonic equation is an important generalization of the p-harmonic equation in R, p > 1, and the p-harmonic equation is a natural extension of the usual Laplace equation see 1 for the details . The reverse Hölder inequalities have been widely studied and frequently used in analysis an...

Intrinsic Hölder continuity of harmonic functions

In a setting, where only “exit measures” are given, as they are associated with a right continuous strong Markov process on a separable metric space, we provide simple criteria for scaling invariant Hölder continuity of bounded harmonic functions with respect to a distance function which, in applications, may be adapted to the special situation. In particular, already a very weak scaling proper...

Harnack inequality and Hölder regularity estimates for a Lévy process with small jumps of high intensity

We consider a Lévy process in Rd (d ≥ 3) with the characteristic exponent Φ(ξ) = |ξ|2 ln(1 + |ξ|2) − 1. The scale invariant Harnack inequality and apriori estimates of harmonic functions in Hölder spaces are proved. AMS Subject Classification: Primary 60J45, Secondary 60G50, 60G51, 60J25, 60J27

To appear in J.Diff.Geom. HÖLDER ESTIMATES AND REGULARITY FOR HOLOMORPHIC AND HARMONIC FUNCTIONS