Article contents
The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1985
References
- 2
- Cited by