Some identities on weighted Sobolev spaces

Tahar Z. Boulmezaoud; Amel Kourta

doi:10.3934/dcdss.2012.5.427

Article Contents

2012, Volume 5, Issue 3: 427-434. Doi: 10.3934/dcdss.2012.5.427

This issue Previous Article On the instability of a nonlocal conservation law Next Article An existence theorem for the magneto-viscoelastic problem

Some identities on weighted Sobolev spaces

Tahar Z. Boulmezaoud^1, and
Amel Kourta^2,

1.
Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines, 45, Avenue des Etats-Unis, 78035, Versailles Cedex
2.
Université de Constantine, Départment de mathématiques, Route ain el bey, 25000, Constantine

Received: August 31, 2010

Revised: December 31, 2010

Published: May 2012

Abstract Related Papers Cited by

Abstract

In this paper we compare some families of weigthted Sobolev spaces which are commonly used for solving partial differential equations in unbounded domains. The first result is an identity between two particular spaces. The second result is another identity which generalises partially the first one.

Keywords:

Mathematics Subject Classification: 46A99, 46N20, 46B50, 46B70.

Citation:

Related Papers

Cited by

References

[1]	C. Amrouche, V. Girault and J. Giroire, Weighted Sobolev spaces for Laplace's equation in $R^n$, J. Math. Pures Appl. (9), 73 (1994), 579-606.
[2]	T. Z. Boulmezaoud and M. Medjden, Vorticity-vector potential formulations of the Stokes equations in the half-space, Mathematical Methods in the Applied Sciences, 28 (2005), 903-915.doi: 10.1002/mma.596.
[3]	T. Z. Boulmezaoud, Espaces de Sobolev avec poids pour l'équation de Laplace dans le demi-espace, Comptes Rendus de l'Académie des Sciences Série I Mathématiques, 328 (1999), 221-226.
[4]	T. Z. Boulmezaoud, On the Laplace operator and on the vector potential problems in the half-space: An approach using weighted spaces, Mathematical Methods in the Applied Sciences, 26 (2003), 633-669.doi: 10.1002/mma.369.
[5]	T. Z. Boulmezaoud and U. Razafison, On the steady Oseen problem in the whole space, Hiroshima Mathematical Journal, 35 (2005), 371-401.
[6]	R. Farwig and H. Sohr, An approach to resolvent estimates for the Stokes equations in $L^q$-spaces, In "The Navier-Stokes Equations II-Theory and Numerical Methods" (Oberwolfach, 1991), Lecture Notes in Math., 1530, Springer, Berlin, (1992), 97-110.
[7]	J. Giroire, "Etude de Quelques Problèmes aux Limites Extérieurs et Résolution par Équations Intégrales", Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris, 1987.
[8]	V. Girault, The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of $R^3$, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 39 (1992), 279-307.
[9]	B. Hanouzet, Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace, Rend. Sem. Mat. Univ. Padova, 46 (1971), 227-272.
[10]	J. G. Heywood, Classical solutions of the Navier-Stokes equations, In "Approximation Methods for Navier-Stokes Problems" (Proc. Sympos., Univ. Paderborn, Paderborn, 1979), Lecture Notes in Math., 771, Springer, Berlin-New York, (1980), 235-248.
[11]	V. A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskov. Mat. Obšč., 16 (1967), 209-292.
[12]	A. Kufner, "Weighted Sobolev Spaces," A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1985.
[13]	V. G. Maz'ja and B. A. Plamenevskiĭ, Weighted spaces with inhomogeneous norms, and boundary value problems in domains with conical points, In "Elliptische Differentialgleichungen" (Meeting, Rostock, 1977), 161-190, Wilhelm-Pieck-Univ., Rostock, 1978.