APPROXIMATION OF HARMONIC FUNCTIONS CLASSES WITH SINGULARITIES ON QUASICONFORMAL CURVES

Solution of Harmonic Problems with Weak Singularities Using Equilibrated Basis Functions in Finite Element Method

In this paper, Equilibrated Singular Basis Functions (EqSBFs) are implemented in the framework of the Finite Element Method (FEM), which can approximately satisfy the harmonic PDE in homogeneous and heterogeneous media. EqSBFs are able to automatically reproduce the terms consistent with the singularity order in the vicinity of the singular point. The newly made bases are used as the compliment...

Quasiconformal Harmonic Functions between Convex Domains

We generalize Martio’s paper [14]. Indeed the problem studied in this paper is under which conditions on a homeomorphism f between the unit circle S1 := {z : |z| = 1} and a fix convex Jordan curve γ the harmonic extension of f is a quasiconformal mapping. In addition, we give some results for some classes of harmonic diffeomorphisms. Further, we give some results concerning harmonic quasiconfor...

Quasiconformal Approximation by Eremenko-lyubich Functions

We discuss a method for constructing functions in the EremenkoLyubich class of transcendental functions with bounded singular set whose infinite tracts have prescribed geometry. Date: Nov 2011. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

On a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator

In this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎Some of our results improve‎ ‎and generalize previously known results‎.

Boundary singularities of N -harmonic functions