# Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition

Chérif Amrouche; Nečasová, Šárka

Mathematica Bohemica (2001)

- Volume: 126, Issue: 2, page 265-274
- ISSN: 0862-7959

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topAmrouche, Chérif, and Nečasová, Šárka. "Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition." Mathematica Bohemica 126.2 (2001): 265-274. <http://eudml.org/doc/248846>.

@article{Amrouche2001,

abstract = {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.},

author = {Amrouche, Chérif, Nečasová, Šárka},

journal = {Mathematica Bohemica},

keywords = {the Laplace equation; weighted Sobolev spaces; the half space; existence; uniqueness; regularity; Laplace equation; weighted Sobolev spaces; half space; existence; uniqueness; regularity},

language = {eng},

number = {2},

pages = {265-274},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition},

url = {http://eudml.org/doc/248846},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Amrouche, Chérif

AU - Nečasová, Šárka

TI - Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 2

SP - 265

EP - 274

AB - 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.

LA - eng

KW - the Laplace equation; weighted Sobolev spaces; the half space; existence; uniqueness; regularity; Laplace equation; weighted Sobolev spaces; half space; existence; uniqueness; regularity

UR - http://eudml.org/doc/248846

ER -

## References

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- 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. (1999) Zbl0924.35033MR1674531
- Espaces de Sobolev avec poids. Application au problème de Dirichlet dans un demi-espace, Rend. Sem. Univ. Padova 46 (1971), 227–272. (1971) MR0310417
- The three-dimensional problem of steady-state motion of a fluid with a free surface, Amer. Math. Soc. Transl. 123 (1984), 171–268. (1984)
- 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. (1996) MR1454361

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