A Note on the Boundary Behaviour of Harmonic Functions

1992 ◽  
Vol s2-46 (2) ◽  
pp. 295-300 ◽  
Author(s):  
J. L. Fernández ◽  
J. G. Llorente
Keyword(s):  
Harmonic Functions ◽  
Boundary Behaviour

A boundary estimate for harmonic functions

1982 ◽  
Vol 91 (1) ◽  
pp. 79-90 ◽  
Author(s):  
P. J. Rippon
Keyword(s):  
Euclidean Space ◽  
Harmonic Functions ◽  
Conformal Mappings ◽  
Dimensional Euclidean Space ◽  
Boundary Behaviour ◽  
Boundary Estimate ◽  
Distortion Theorems

In this paper we extend to certain domains in m-dimensional Euclidean space Rm, m ≥ 3, some results about the boundary behaviour of harmonic functions which, in R2, are known to follow from distortion theorems for conformal mappings.

scholarly journals Boundary behaviour of harmonic functions and solutions of parabolic systems

1988 ◽  
Vol 31 (2) ◽  
pp. 267-270
Author(s):  
N. A. Watson
Keyword(s):  
Harmonic Function ◽  
Harmonic Functions ◽  
Parabolic Systems ◽  
Boundary Behaviour ◽  
Nontangential Limit ◽  
Nontangential Limits

In [1], Calderón proved that, if u is a harmonic function on Rn × ]0, ∞[, and at each point ξ of a subset E of Rn, u is bounded in some cone with vertex (ξ, 0), then u has a nontangential limit at almost every point of E × {0}. The main result of this note is a stronger version of this theorem, in which the hypotheses remain unchanged but the nontangential limits in the conclusion are replaced by limits through the more general approach regions first considered by Nagel and Stein in [7].

scholarly journals AREA INTEGRALS AND BOUNDARY BEHAVIOUR OF HARMONIC FUNCTIONS

2004 ◽  
Vol 47 (2) ◽  
pp. 365-373
Author(s):  
Mary Hanley
Keyword(s):  
Half Space ◽  
Harmonic Functions ◽  
Subject Classification ◽  
Boundary Behaviour ◽  
Primary 31B25

AbstractThis paper introduces a family of area-type integrals over cones. These are used to investigate non-tangential boundary behaviour of harmonic functions on a half-space, extending results of Stein and Brossard.AMS 2000 Mathematics subject classification: Primary 31B25

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