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Radial limits of positive solutions to the Darboux equation

Authors:

E S Dubtsov

Institution:

(1) St.Peterburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

Abstract:

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. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 355, 2008, pp. 163–172.

Keywords:

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