-
Previous Article
A variational convergence for bifunctionals. Application to a model of strong junction
- DCDS-S Home
- This Issue
-
Next Article
Preface
Elliptic problems with $L^1$-data in the half-space
1. | Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l’Adour, IPRA, Avenue de l’Université, 64000 Pau |
2. | Departamento de Matematica, IMECC - Universidade Estadual de Campinas, Caixa Postal 6065, Campinas, SP 13083-970, Brazil |
References:
[1] |
R. A. Adams and J. J. Fournier, "Sobolev Spaces," Second edition, Pure and Applied Mathematics (Amsterdam), 140, Elsevier/Academic Press, Amsterdam, 2003. |
[2] |
C. Amrouche, The Neumann problem in the half-space, Comptes Rendus de l'Académie des Sciences de Paris, 335 (2002), 151-156. |
[3] |
C. Amrouche, V. Girault and J. Giroire, Weighted Sobolev spaces for Laplace's equation in $\R^n$, Journal de Mathématiques Pures et Appliquées (9), 73 (1994), 579-606. |
[4] |
C. Amrouche, V. Girault and J. Giroire, Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: An approach in weighted Sobolev spaces, Journal de Mathématiques Pures et Appliquées (9), 76 (1997), 55-81.
doi: 10.1016/S0021-7824(97)89945-X. |
[5] |
C. Amrouche and Š. Nečasová, Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition, Proceedings of Partial Differential Equations and Applications (Olomouc, 1999), Mathematica Bohemica, 126 (2001), 265-274. |
[6] |
C. Amrouche, Š. Nečasová and Y. Raudin, Very weak, generalized and strong solutions to the Stokes system in the half-space, Journal of Differential Equations, 244 (2008), 887-915.
doi: 10.1016/j.jde.2007.10.007. |
[7] |
C. Amrouche, Š. Nečasová and Y. Raudin, From strong to very weak solutions to the Stokes system with Navier boundary conditions in the half-space, SIAM J. Math. Anal., 41 (2009), 1792-1815.
doi: 10.1137/090749207. |
[8] |
J. Bourgain and H. Brezis, On the equation div $Y=f$ and application to control of phases, Journal of the American Mathematical Society, 16 (2003), 393-426.
doi: 10.1090/S0894-0347-02-00411-3. |
[9] |
J. Bourgain and H. Brezis, New estimates for elliptic equations and Hodge type systems, Journal of the European Mathematical Society, 9 (2007), 277-315.
doi: 10.4171/JEMS/80. |
[10] |
J. Bourgain and H. Brezis, Sur l'équation div $u=f$, Comptes Rendus de l'Académie des Sciences de Paris, 334 (2002), 973-976. |
[11] |
J. Bourgain and H. Brezis, New estimates for the Laplacian, the div-curl, and related Hodge systems, Comptes Rendus de l'Académie des Sciences de Paris, 338 (2004), 539-543. |
[12] |
H. Brezis and J. Van Schaftingen, Boundary extimates for elliptic systems with $\mathbfL^1$-data, Calculus of Variations and Partial Differential Equations, 30 (2007), 369-388.
doi: 10.1007/s00526-007-0094-9. |
[13] |
J. Deny and J. L. Lions, Les espaces du type de Beppo Levi,, Annales de l'Institut Fourier, 5 (): 1953.
doi: 10.5802/aif.55. |
[14] |
V. Girault, The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of $\mathbbR^3$, Journal of the Faculty of Science, The University of Tokyo, Sect. IA Math., 39 (1992), 279-307. |
[15] |
B. Hanouzet, Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace, Rendiconti del Seminario Matematico della Université di Padova, 46 (1971), 227-272. |
[16] |
J. Van Schaftingen, Estimates for $L^1$-vector fields, Comptes Rendus de l'Académie des Sciences de Paris, 339 (2004), 181-186. |
show all references
References:
[1] |
R. A. Adams and J. J. Fournier, "Sobolev Spaces," Second edition, Pure and Applied Mathematics (Amsterdam), 140, Elsevier/Academic Press, Amsterdam, 2003. |
[2] |
C. Amrouche, The Neumann problem in the half-space, Comptes Rendus de l'Académie des Sciences de Paris, 335 (2002), 151-156. |
[3] |
C. Amrouche, V. Girault and J. Giroire, Weighted Sobolev spaces for Laplace's equation in $\R^n$, Journal de Mathématiques Pures et Appliquées (9), 73 (1994), 579-606. |
[4] |
C. Amrouche, V. Girault and J. Giroire, Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: An approach in weighted Sobolev spaces, Journal de Mathématiques Pures et Appliquées (9), 76 (1997), 55-81.
doi: 10.1016/S0021-7824(97)89945-X. |
[5] |
C. Amrouche and Š. Nečasová, Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition, Proceedings of Partial Differential Equations and Applications (Olomouc, 1999), Mathematica Bohemica, 126 (2001), 265-274. |
[6] |
C. Amrouche, Š. Nečasová and Y. Raudin, Very weak, generalized and strong solutions to the Stokes system in the half-space, Journal of Differential Equations, 244 (2008), 887-915.
doi: 10.1016/j.jde.2007.10.007. |
[7] |
C. Amrouche, Š. Nečasová and Y. Raudin, From strong to very weak solutions to the Stokes system with Navier boundary conditions in the half-space, SIAM J. Math. Anal., 41 (2009), 1792-1815.
doi: 10.1137/090749207. |
[8] |
J. Bourgain and H. Brezis, On the equation div $Y=f$ and application to control of phases, Journal of the American Mathematical Society, 16 (2003), 393-426.
doi: 10.1090/S0894-0347-02-00411-3. |
[9] |
J. Bourgain and H. Brezis, New estimates for elliptic equations and Hodge type systems, Journal of the European Mathematical Society, 9 (2007), 277-315.
doi: 10.4171/JEMS/80. |
[10] |
J. Bourgain and H. Brezis, Sur l'équation div $u=f$, Comptes Rendus de l'Académie des Sciences de Paris, 334 (2002), 973-976. |
[11] |
J. Bourgain and H. Brezis, New estimates for the Laplacian, the div-curl, and related Hodge systems, Comptes Rendus de l'Académie des Sciences de Paris, 338 (2004), 539-543. |
[12] |
H. Brezis and J. Van Schaftingen, Boundary extimates for elliptic systems with $\mathbfL^1$-data, Calculus of Variations and Partial Differential Equations, 30 (2007), 369-388.
doi: 10.1007/s00526-007-0094-9. |
[13] |
J. Deny and J. L. Lions, Les espaces du type de Beppo Levi,, Annales de l'Institut Fourier, 5 (): 1953.
doi: 10.5802/aif.55. |
[14] |
V. Girault, The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of $\mathbbR^3$, Journal of the Faculty of Science, The University of Tokyo, Sect. IA Math., 39 (1992), 279-307. |
[15] |
B. Hanouzet, Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace, Rendiconti del Seminario Matematico della Université di Padova, 46 (1971), 227-272. |
[16] |
J. Van Schaftingen, Estimates for $L^1$-vector fields, Comptes Rendus de l'Académie des Sciences de Paris, 339 (2004), 181-186. |
[1] |
Diego D. Felix, Marcelo F. Furtado, Everaldo S. Medeiros. Semilinear elliptic problems involving exponential critical growth in the half-space. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4937-4953. doi: 10.3934/cpaa.2020219 |
[2] |
Vasily Denisov and Andrey Muravnik. On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations. Electronic Research Announcements, 2003, 9: 88-93. |
[3] |
Giuseppe Da Prato, Alessandra Lunardi. Maximal dissipativity of a class of elliptic degenerate operators in weighted $L^2$ spaces. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 751-760. doi: 10.3934/dcdsb.2006.6.751 |
[4] |
Ademir Fernando Pazoto, Lionel Rosier. Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1511-1535. doi: 10.3934/dcdsb.2010.14.1511 |
[5] |
Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Selfadjointness of degenerate elliptic operators on higher order Sobolev spaces. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 581-593. doi: 10.3934/dcdss.2011.4.581 |
[6] |
Chérif Amrouche, Yves Raudin. Singular boundary conditions and regularity for the biharmonic problem in the half-space. Communications on Pure and Applied Analysis, 2007, 6 (4) : 957-982. doi: 10.3934/cpaa.2007.6.957 |
[7] |
Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the half-space. Communications on Pure and Applied Analysis, 2014, 13 (2) : 511-525. doi: 10.3934/cpaa.2014.13.511 |
[8] |
Gershon Kresin, Vladimir Maz’ya. Optimal estimates for the gradient of harmonic functions in the multidimensional half-space. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 425-440. doi: 10.3934/dcds.2010.28.425 |
[9] |
Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1205-1235. doi: 10.3934/dcds.2019052 |
[10] |
Wenning Wei. On the Cauchy-Dirichlet problem in a half space for backward SPDEs in weighted Hölder spaces. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5353-5378. doi: 10.3934/dcds.2015.35.5353 |
[11] |
Tahar Z. Boulmezaoud, Amel Kourta. Some identities on weighted Sobolev spaces. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 427-434. doi: 10.3934/dcdss.2012.5.427 |
[12] |
Kyeong-Hun Kim, Kijung Lee. A weighted $L_p$-theory for second-order parabolic and elliptic partial differential systems on a half space. Communications on Pure and Applied Analysis, 2016, 15 (3) : 761-794. doi: 10.3934/cpaa.2016.15.761 |
[13] |
Doyoon Kim, Hongjie Dong, Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4895-4914. doi: 10.3934/dcds.2016011 |
[14] |
Jun Yang, Yaotian Shen. Weighted Sobolev-Hardy spaces and sign-changing solutions of degenerate elliptic equation. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2565-2575. doi: 10.3934/cpaa.2013.12.2565 |
[15] |
T. V. Anoop, Nirjan Biswas, Ujjal Das. Admissible function spaces for weighted Sobolev inequalities. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3259-3297. doi: 10.3934/cpaa.2021105 |
[16] |
Doyoon Kim, Kyeong-Hun Kim, Kijung Lee. Parabolic Systems with measurable coefficients in weighted Sobolev spaces. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022062 |
[17] |
Niclas Bernhoff. On half-space problems for the weakly non-linear discrete Boltzmann equation. Kinetic and Related Models, 2010, 3 (2) : 195-222. doi: 10.3934/krm.2010.3.195 |
[18] |
Yanqin Fang, Jihui Zhang. Nonexistence of positive solution for an integral equation on a Half-Space $R_+^n$. Communications on Pure and Applied Analysis, 2013, 12 (2) : 663-678. doi: 10.3934/cpaa.2013.12.663 |
[19] |
Ziwei Zhou, Jiguang Bao, Bo Wang. A Liouville theorem of parabolic Monge-AmpÈre equations in half-space. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1561-1578. doi: 10.3934/dcds.2020331 |
[20] |
Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the half-space inverse scattering problem with phaseless data. Inverse Problems and Imaging, 2017, 11 (5) : 901-916. doi: 10.3934/ipi.2017042 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]