Artículos de revistas
Elliptic Problems With L1-data In The Half-space
Registro en:
Discrete And Continuous Dynamical Systems - Series S. , v. 5, n. 3, p. 369 - 397, 2012.
19371632
10.3934/dcdss.2012.5.369
2-s2.0-84864459586
Autor
Amrouche C.
Nguyen H.H.
Institución
Resumen
In this paper, we study the div-curl-grad operators and some el- liptic problems in the half-space Rn +, with n 2. We consider data in weighted Sobolev spaces and in L1. 5 3 369 397 Adams, R.A., Fournier, J.J., (2003) Sobolev Spaces," Second Edition, Pure and Applied Math- Ematics (Amsterdam), p. 140. , Elsevier/Academic Press, Amsterdam Amrouche, C., The Neumann problem in the half-space (2002) Comptes Rendus Mathematique, 335 (2), pp. 151-156. , DOI 10.1016/S1631-073X(02)02428-7, PII S1631073X02024287 Amrouche, C., Girault, V., Giroire, J., Weighted Sobolev spaces for Laplace's equation in Rn (1994) Journal de Mathematiques Pures et Appliquees (9), 73, 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) Journal des Mathematiques Pures et Appliquees, 76 (1), pp. 55-81 Amrouche, C., Necasova, S., Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition (2001) Proceedings of Partial Differential Equations and Applications (Olomouc, 1999), Mathematica Bohemica, 126, pp. 265-274 Amrouche, C., Necasova, S., Raudin, Y., Very weak, generalized and strong solutions to the Stokes system in the half-space (2008) Journal of Differential Equations, 244, pp. 887-915 Amrouche, C., Necasova, S., 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, pp. 1792-1815 Bourgain, J., Brezis, H., On the equation div Y = f and application to control of phases (2003) Journal of the American Mathematical Society, 16 (2), pp. 393-426. , DOI 10.1090/S0894-0347-02-00411-3 Bourgain, J., Brezis, H., New estimates for elliptic equations and Hodge type systems (2007) Journal of the European Mathematical Society, 9, pp. 277-315 Bourgain, J., Brezis, H., Sur l'equation div u = f (2002) Comptes Rendus de l'Academie des Sciences de Paris, 334, pp. 973-976 Bourgain, J., Brezis, H., New estimates for the Laplacian, the div-curl, and related Hodge systems (2004) Comptes Rendus Mathematique, 338 (7), pp. 539-543. , DOI 10.1016/j.crma.2003.12.031, PII S1631073X04000329 Brezis, H., Van Schaftingen, J., Boundary extimates for elliptic systems with L1-data (2007) Calculus of Variations and Partial Differential Equations, 30, pp. 369-388 Deny, J., Lions, J.L., Les espaces du type de Beppo Levi (1953) Annales de l'Institut Fourier, Grenoble, 5, pp. 305-370 Girault, V., The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of R3 (1992) Journal of the Faculty of Science, 39, pp. 279-307. , The University of Tokyo, Sect. IA Math Hanouzet, B., Espaces de Sobolev avec poids application au probleme de Dirichlet dans un demi espace (1971) Rendiconti Del Seminario Matematico della Universite di Padova, 46, pp. 227-272 Van Schaftingen, J., Estimates for L1-vector elds (2004) Comptes Rendus de l'Academie des Sci- Ences de Paris, 339, pp. 181-186