Geodesic
The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition
Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 113-119

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1985-013-1
Mots-clés : 31A20, 26A39 
Benedicks, M.; Pfeffer, W. F. The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition. Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 113-119. doi: 10.4153/CMB-1985-013-1
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