Artículos de revistas
New Estimates For The Div-curl-grad Operators And Elliptic Problems With L1-data In The Whole Space And In The Half-space
Registro en:
Journal Of Differential Equations. , v. 250, n. 7, p. 3150 - 3195, 2011.
220396
10.1016/j.jde.2011.01.012
2-s2.0-79951557063
Autor
Amrouche C.
Nguyen H.H.
Institución
Resumen
In this paper, we study the div-curl-grad operators and some elliptic problems in the whole space Rn and in the half-space R+n, with n≥2. We consider data in weighted Sobolev spaces and in L1. © 2011 Elsevier Inc. 250 7 3150 3195 Adams, R.A., (2003) Sobolev Spaces, , Academic Press, New York Alliot, F., Amrouche, C., The Stokes problem in Rn: an approach in weighted Sobolev spaces (1999) Math. Models Methods Appl. Sci., 9, pp. 723-754 Amrouche, C., The Neumann problem in the half-space (2002) C. R. Acad. Sci. Paris, I 335, pp. 151-156 Amrouche, C., Girault, V., Giroire, J., Weighted Sobolev spaces for the Laplace equation in Rn (1994) J. Math. Pures Appl., 73 (6), pp. 579-606 Amrouche, C., Girault, V., Giroire, J., Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: an approach in weighted Sobolev spaces (1997) J. Math. Pures Appl., 76 (1), pp. 55-81 Amrouche, C., Neasová, S., Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition (2001) Math. Bohem., 126 (2), pp. 265-274 Amrouche, C., Neasová, S., Raudin, Y., Very weak, generalized and strong solutions to the Stokes system in the half-space (2008) J. Differential Equations, 244, pp. 887-915 Amrouche, C., Raudin, Y., From strong to very weak solutions to the Stokes system with Navier boundary conditions in the half-space (2009) SIAM J. Math. Anal., 41 (5), pp. 1792-1815 Amrouche, C., Razafison, U., The stationary Oseen equations in R3. An approach in weighted Sobolev spaces (2007) J. Math. Fluids Mech., 9 (2), pp. 211-225 Bourgain, J., Brézis, H., On the equation divY=f and application to control of phases (2002) J. Amer. Math. Soc., 16 (2), pp. 393-426 Bourgain, J., Brézis, H., New estimates for elliptic equations and Hodge type systems (2007) J. Eur. Math. Soc. (JEMS), 9 (2), pp. 277-315 Bourgain, J., Brézis, H., Sur l'équation divu=f (2002) C. R. Acad. Sci. Paris, I 334, pp. 973-976 Bourgain, J., Brézis, H., New estimates for the Laplacian, the div-curl, and related Hodge systems (2003) C. R. Acad. Sci. Paris, I 338, pp. 539-543 Brézis, H., (1999) Analyse fonctionnelle: Théorie et applications, , Dunod, Paris Brézis, H., Van Schaftingen, J., Boundary estimates for elliptic systems with L1-data (2007) Calc. Var. Partial Differential Equations, 30 (3), pp. 369-388 Deny, J., Lions, J.L., Les espaces du type de Beppo Levi (1954) Ann. Inst. Fourier (Grenoble), 5, pp. 305-370 Girault, V., The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of R3 (1992) J. Math. Sci. Univ. Tokyo (Sec. IA), 39 (2), pp. 279-307 Hanouzet, B., Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace (1971) Rend. Semin. Mat. Univ. Padova, 46, pp. 227-272 Miyakawa, T., Hardy spaces of solenoidal vector fields, with applications to the Navier-Stokes equations (1996) Kyushu J. Math., 50, pp. 1-64 Miyakawa, T., On L1-stability of stationary Navier-Stokes flows in Rn (1997) J. Math. Sci. Univ. Tokyo, 4, pp. 67-119 Payne, L.E., Weinberger, H.F., Note on a lemma of Finn and Gilbarg (1957) Acta Math., 98, pp. 297-299 Van Schaftingen, J., Estimates for L1-vector fields (2004) C. R. Acad. Sci. Paris, I 339, pp. 181-186