Regularity of $p$-Harmonic Functions on the Plane

ON THE REGULARITY OF p-HARMONIC FUNCTIONS IN THE HEISENBERG GROUP by

On the Linear Combinations of Slanted Half-Plane Harmonic Mappings

‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.

ON THE REGULARITY OF SUBELLIPTIC p-HARMONIC FUNCTIONS IN CARNOT GROUPS

In this paper we prove second order horizontal differentiability and C1,α regularity results for subelliptic p-harmonic functions in Carnot groups for p close to 2.

α - regularity for p - harmonic functions in the Heisenberg group for p near 2

We prove C1,α regularity for p-harmonic functions in the Heisenberg group for p in a neighborhood of 2.

Positive Harmonic Functions on Denjoy Domains in the Complex Plane

Let Ω be a domain in the complex plane C whose complement E = C \ Ω, where C = C ∪ {∞} is a subset of the real line (i.e. Ω is a Denjoy domain). If each point of E is regular for the Dirichlet problem in Ω, we provide a geometric description of the structure of E near infinity such that the Martin boundary of Ω has one or two “infinite” points.