Geodesic
Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition
Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 265-274

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
We deal with the Laplace equation in the half space. The use of a special family of weigted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet problem.
We deal with the Laplace equation in the half space. The use of a special family of weigted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet problem.
DOI : 10.21136/MB.2001.134013
Classification : 35A05, 35B65, 35J05, 35J25, 58J10
Keywords: the Laplace equation; weighted Sobolev spaces; the half space; existence; uniqueness; regularity 
Amrouche, Cherif; Nečasová, Šárka. Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition. Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 265-274. doi: 10.21136/MB.2001.134013
@article{10_21136_MB_2001_134013,
     author = {Amrouche, Cherif and Ne\v{c}asov\'a, \v{S}\'arka},
     title = {Laplace equation in the half-space with a~nonhomogeneous {Dirichlet} boundary condition},
     journal = {Mathematica Bohemica},
     pages = {265--274},
     year = {2001},
     volume = {126},
     number = {2},
     doi = {10.21136/MB.2001.134013},
     mrnumber = {1844267},
     zbl = {0979.35038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134013/}
}
TY  - JOUR
AU  - Amrouche, Cherif
AU  - Nečasová, Šárka
TI  - Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition
JO  - Mathematica Bohemica
PY  - 2001
SP  - 265
EP  - 274
VL  - 126
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134013/
DO  - 10.21136/MB.2001.134013
LA  - en
ID  - 10_21136_MB_2001_134013
ER  - 
%0 Journal Article
%A Amrouche, Cherif
%A Nečasová, Šárka
%T Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition
%J Mathematica Bohemica
%D 2001
%P 265-274
%V 126
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134013/
%R 10.21136/MB.2001.134013
%G en
%F 10_21136_MB_2001_134013

[1] C. Amrouche, V. Girault, J. Giroire: Weighted Sobolev spaces for Laplace’s equation in $\mathbb{R}^N$. J. Math. Pures Appl. 73 (1994), 579–606. | MR

[2] T. Z. Boulmezaoud: Espaces de Sobolev avec poids pour l’équation de Laplace dans le demi-espace. C. R. Acad. Sci. Paris, Ser. I 328 (1999), 221–226. | DOI | MR | Zbl

[3] B. Hanouzet: Espaces de Sobolev avec poids. Application au problème de Dirichlet dans un demi-espace. Rend. Sem. Univ. Padova 46 (1971), 227–272. | MR

[4] V. G. Maz’ya, B. A. Plamenevskii, L. I. Stupyalis: The three-dimensional problem of steady-state motion of a fluid with a free surface. Amer. Math. Soc. Transl. 123 (1984), 171–268. | DOI

[5] C. C. Simader, H. Sohr: The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains. Pitman Research Notes in Matehmatics Series 360, Addison Wesley Longman, Harlow, Great Britain, 1996. | MR

Cité par Sources :