相关论文: Uniqueness theorem for unbounded domain

In this paper we prove that bounded Hua-harmonic functions on tube domains that satisfy some boundary regularity condition are necessarily pluriharmonic. In doing so, we show that a similar theorem is true on one-dimensional extensions of…

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…

Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.

For families of continuous plurisubharmonic functions we show that, in a local sense, separately bounded above implies bounded above.

We investigate the boundary behavior of holomorphic functions with respect to a family of curves in a domain of finite type. This work is a generalization of \u{C}irka's classical result on the unit ball and it supplements the result by…

We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic…

We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.

This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

A monotonicity property of Harnack inequality is proved for positive invariant harmonic functions in the unit ball.

We prove a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient boundary blow up rates for…

We give examples of $L^{1}$-functions that are essentially unbounded on every nonempty open subset of their domains of definition. We obtain such functions as limits of weighted sums of functions with the unboundedly increasing number of…

The aim of this note is to explain a generalization to the real case of a well known result on the automorphism group of an unbounded tube type symmetric domain in a complex vector space of finite dimension.

We give several generalizations of Rellich's classical uniqueness theorem to unbounded domains. We give a natural half-space generalization for super-exponentially decaying inhomogeneities using real variable techniques. We also prove under…

In this paper, we study the infinity harmonic functions with linear growth rate at infinity defined on exterior domains. We show that such functions must be asymptotic to planes or cones at infinity. We also establish the solvability of…

The Riemann Theorem states, that for any nontrivial connected and simply connected domain on the Riemann sphere there exists some its conformal bijection to the exterior of the unit disk. In this paper we find an explicit form of this map…

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.

We determine the automorphism groups of unbounded homogeneous domains with boundaries of light cone type. Furthermore we present the group-theoretic characterization of the domain. As a corollary we prove the non-existence of compact…

The classical Fatou theorem identifies bounded harmonic functions on the unit disk with bounded measurable functions on the boundary circle. We extend this theorem to bounded harmonic maps.