Analysis Mathematica

, Volume 21, Issue 2, pp 101–106 | Cite as

О граничном поведени и неограниченных супергармонических функций

  • Э. А. Кулиев
Article
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On boundary behaviour of unbounded superharmonic functions

Abstract

In this paper it is proved that a function, superharmonic on a domain inRn+1 with Lipschitz boundary, cannot have nontangential limit equal to +∞ on a set of positiven-dimensional measure on the boundary. As a corollary, a generalization of the uniqueness theorem of Lusin-Privalov on the nontangential limits of functions, analytic on a domain in the complex plane, is obtained for the case of functions, analytic on a domain in C n (n>1) with Lipschitz boundary. Formulation of a generalization of the main theorem is also given for the case of the solutions of uniformly elliptic equations with infinitely smooth coefficients.

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Литература

  1. [1]
    B. Dahlberg, Harmonic functions in Lipschitz domains,Proc. Symp. in Pure Math.,35(1)(1979), 313–322.Google Scholar
  2. [2]
    M. Г. Голузина, Теоре ма Лузина-Привалова д ля субгармонических функций,Матем. замет ки,47(4)(1960), 157–159.Google Scholar
  3. [3]
    D. Jerison andC. Kenig, The Dirichlet problem in nonsmooth domains,Annals of Math.,113(1981), 367–382.Google Scholar

Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Э. А. Кулиев
    • 1
  1. 1.ИНСТИТУТ МАТЕМТИКИ И МЕХАНИКИ АН АЗЕРБАЙДЖАНАБАКУАЗЕРБАЙДЖАН

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