The P-harmonic System with Measure-valued Right Hand Side

Uniqueness and Maximal Regularity for Nonlinear Elliptic Systems of N-laplace Type with Measure Valued Right Hand Side

On the averaging of differential inclusions with Fuzzy right hand side with the average of the right hand side is absent

In this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist. 

Regularity of generalized sphere valued p - harmonic maps with small mean oscillations

We prove (see Theorem 1.3 below) that a generalized harmonic map into a round sphere, i.e. a map u ∈ W 1,1 loc ( , Sn−1) which solves the system div (ui∇uj − uj∇ui) = 0, i, j = 1, . . . , n, is smooth as soon as |∇u| ∈ L for any q > 1, and the norm of u in BMO is sufficiently small. Here, ⊂ R is open, and m, n are arbitrary. This extends various earlier results of Almeida [1], Ge [15], and R. M...

0 v 1 [ m at h . PR ] 1 5 O ct 2 00 3 The harmonic explorer and its convergence to SLE ( 4 ) Oded

The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE4 as the grid gets finer.

A new subclass of harmonic mappings with positive coefficients

‎Complex-valued harmonic functions that are univalent and‎ ‎sense-preserving in the open unit disk $U$ can be written as form‎ ‎$f =h+bar{g}$‎, ‎where $h$ and $g$ are analytic in $U$‎. ‎In this paper‎, ‎we introduce the class $S_H^1(beta)$‎, ‎where $1<betaleq 2$‎, ‎and‎ ‎consisting of harmonic univalent function $f = h+bar{g}$‎, ‎where $h$ and $g$ are in the form‎ ‎$h(z) = z+sumlimits_{n=2}^inf...