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Some identities on weighted Sobolev spaces
| 1. | Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines, 45, Avenue des Etats-Unis, 78035, Versailles Cedex, France |
| 2. | Université de Constantine, Départment de mathématiques, Route ain el bey, 25000, Constantine, Algeria |
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. |
show all references
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. |
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