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

DOI

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
@article{10_4153_CMB_1985_013_1,
     author = {Benedicks, M. and Pfeffer, W. F.},
     title = {The {Dirichlet} {Problem} {With} {Denjoy-Perron} {Integrable} {Boundary} {Condition}},
     journal = {Canadian mathematical bulletin},
     pages = {113--119},
     year = {1985},
     volume = {28},
     number = {1},
     doi = {10.4153/CMB-1985-013-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-013-1/}
}
TY  - JOUR
AU  - Benedicks, M.
AU  - Pfeffer, W. F.
TI  - The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition
JO  - Canadian mathematical bulletin
PY  - 1985
SP  - 113
EP  - 119
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-013-1/
DO  - 10.4153/CMB-1985-013-1
ID  - 10_4153_CMB_1985_013_1
ER  - 
%0 Journal Article
%A Benedicks, M.
%A Pfeffer, W. F.
%T The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition
%J Canadian mathematical bulletin
%D 1985
%P 113-119
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-013-1/
%R 10.4153/CMB-1985-013-1
%F 10_4153_CMB_1985_013_1

Cité par Sources :