One-Sided Boundary Behavior for Certain Harmonic Functions

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.  

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.

Blow-up behavior of Planar Harmonic Functions Satisfying a Certain Exponential Neumann Boundary Condition

In this paper we provide a detailed analysis of the limiting behaviour of some very general families of solutions to the boundary value problem ∆v = 0 in Ω, ∂v/∂n = λ sinh(v) on ∂Ω, as λ → 0. The existence of countably many of these families has already been established in the papers [4] and [6].

Certain Convex Harmonic Functions

Boundary Behavior of Harmonic Functions for Truncated Stable Processes

For any α ∈ (0, 2), a truncated symmetric α-stable process in R is a symmetric Lévy process in R with no diffusion part and with a Lévy density given by c|x| 1{|x|<1} for some constant c. In [24] we have studied the potential theory of truncated symmetric stable processes. Among other things, we proved that the boundary Harnack principle is valid for the positive harmonic functions of this proc...