Advanced Search
Article Contents
Article Contents

Some identities on weighted Sobolev spaces

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: 46A99, 46N20, 46B50, 46B70.


    \begin{equation} \\ \end{equation}
  • [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.


    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.


    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.


    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.


    T. Z. Boulmezaoud and U. Razafison, On the steady Oseen problem in the whole space, Hiroshima Mathematical Journal, 35 (2005), 371-401.


    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.


    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.


    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.


    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.


    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.


    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.


    A. Kufner, "Weighted Sobolev Spaces," A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1985.


    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.

  • 加载中

Article Metrics

HTML views() PDF downloads(102) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint