Asymptotic tracts of harmonic functions I

Asymptotic Behavior of Infinity Harmonic Functions Near an Isolated Singularity

In this paper, we prove that if n ≥ 2 and x0 is an isolated singularity of a non-negative infinity harmonic function u, then either x0 is a removable singularity of u or u(x) = u(x0) + c|x − x0| + o(|x − x0|) near x0 for some fixed constant c = 0. In particular, if x0 is nonremovable, then u has a local maximum or a local minimum at x0. We also prove a Bernstein-type theorem, which asserts that...

A lower estimate of harmonic functions

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Stability for certain subclasses of harmonic univalent functions

In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.

A certain convolution approach for subclasses of univalent harmonic functions

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.