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

Abstract

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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.

How to cite

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Amrouche, 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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  1. Weighted Sobolev spaces for Laplace’s equation in N , J. Math. Pures Appl. 73 (1994), 579–606. (1994) MR1309165
  2. 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
  3. Espaces de Sobolev avec poids. Application au problème de Dirichlet dans un demi-espace, Rend. Sem. Univ. Padova 46 (1971), 227–272. (1971) MR0310417
  4. The three-dimensional problem of steady-state motion of a fluid with a free surface, Amer. Math. Soc. Transl. 123 (1984), 171–268. (1984) 
  5. 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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