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The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition

Published online by Cambridge University Press:  20 November 2018

M. Benedicks  and
W. F. Pfeffer
M. Benedicks
Affiliation:
Chalmers Institute of TechnologyandUniversity of GöteborgGöteborg, Sweden
W. F. Pfeffer
Affiliation:
University of Petroleum and MineralsDhahran, Saudi Arabia
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Abstract

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The Poisson integral of a Denjoy-Perron integrable function defined on the boundary of an open disc is harmonic in this disc. Moreover, almost everywhere on the boundary, the nontangential limits of the integral coincide with the boundary condition. This extends the classical result for Lebesgue integrable boundary conditions. By means of conformai maps, a generalization to domains bounded by a sufficiently smooth Jordan curve is also obtained.

Keywords

31A2026A39
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 1 , 01 March 1985 , pp. 113 - 119
Copyright
Copyright © Canadian Mathematical Society 1985

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