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 ℝ N , J. Math. Pures Appl. 73 (1994), 579–606. (1994) MR1309165
  2. 10.1016/S0764-4442(99)80125-6, C. R. Acad. Sci. Paris, Ser. I 328 (1999), 221–226. (1999) Zbl0924.35033MR1674531DOI10.1016/S0764-4442(99)80125-6
  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. 10.1090/trans2/123/07, Amer. Math. Soc. Transl. 123 (1984), 171–268. (1984) DOI10.1090/trans2/123/07
  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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