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Journal of Mathematical Sciences

, Volume 156, Issue 5, pp 813–818 | Cite as

Radial limits of positive solutions to the Darboux equation

  • E. S. Dubtsov
Article
Assume that a positive function u satisfies the Darboux equation
$$\Delta u = \frac{{\left( {\alpha - 1} \right)}} {y}\frac{{\partial u}} {{\partial y}},\quad \alpha > 0,$$
in the upper half-space ℝ + d+1. We study Bloch type conditions which guarantee the following property: for any a ∈ (0, + ∞), the set on which the radial limit of u is equal to a is large in the sense of the Hausdorff dimension. Bibliography: 6 titles.

Keywords

Russia Positive Function Type Condition Hausdorff Dimension Mathematical Institute 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.St.Peterburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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