| Title:
|
Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition (English) |
| Author:
|
Amrouche, Cherif |
| Author:
|
Nečasová, Šárka |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
265-274 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
the Laplace equation |
| Keyword:
|
weighted Sobolev spaces |
| Keyword:
|
the half space |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
regularity |
| MSC:
|
35A05 |
| MSC:
|
35B65 |
| MSC:
|
35J05 |
| MSC:
|
35J25 |
| MSC:
|
58J10 |
| idZBL:
|
Zbl 0979.35038 |
| idMR:
|
MR1844267 |
| DOI:
|
10.21136/MB.2001.134013 |
| . |
| Date available:
|
2009-09-24T21:50:16Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134013 |
| . |
| Reference:
|
[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 1309165 |
| Reference:
|
[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. Zbl 0924.35033, MR 1674531, 10.1016/S0764-4442(99)80125-6 |
| Reference:
|
[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 0310417 |
| Reference:
|
[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. 10.1090/trans2/123/07 |
| Reference:
|
[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 1454361 |
| . |
