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On the $L^p-$ theory of Anisotropic singular perturbations of elliptic problems
1. | Académie de Grenoble, Lycée Saint-Marc, Nivolas-Vermelle, 38300, France |
References:
[1] |
R.A. Adams and John J.F. Fournier, Sobolev Spaces, Pure and Applied Mathematics, Academic Press, 2003. |
[2] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math, 12 (1959), 623-727. |
[3] |
L. Boccardo, T. Gallouët and J.L. Vazquez, Nonlinear elliptic equations in $R^n$ without growth restrictions on the data, Journal of Differential Equations, 105 (1993), 334-363.
doi: 10.1006/jdeq.1993.1092. |
[4] |
Ph. Bénilan, Philippe, L. Boccardo, Th. Gallouët, R. Gariepy, M. Pierre and J.L. Vazquez, An $L^{1}$-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola. Norm. Sup. Pisa Cl. Sci, 22 (1995), 241-273. |
[5] |
M. Chipot, Elliptic Equations, An Introductory Cours, Birkhauser, ISBN: 978-3764399818, 2009.
doi: 10.1007/978-3-7643-9982-5. |
[6] |
M. Chipot, On some anisotropic singular perturbation problems, Asymptotic Analysis, 55 (2007), 125-144. |
[7] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Acad. Sci. Paris, Ser. I, 346 (2008), 21-26.
doi: 10.1016/j.crma.2007.12.004. |
[8] |
M. Chipot and S. Guesmia, On the asymptotic behaviour of elliptic, anisotropic singular perturbations problems, Com. Pur. App. Ana, 8 (2009), 179-193.
doi: 10.3934/cpaa.2009.8.179. |
[9] |
M. Chipot, S. Guesmia and M. Sengouga, Singular perturbations of some nonlinear problems, J. Math. Sci, 176 2011, 828-843.
doi: 10.1007/s10958-011-0439-y. |
[10] |
M. Chipot and S. Guesmia, On a class of integro-differential problems, Commun. Pure Appl. Anal., 9 2010, 1249-1262.
doi: 10.3934/cpaa.2010.9.1249. |
[11] |
P. Enflo, A counterexample to the approximation problem in Banach spaces, Acta Mathematica, 130 (1973), 309-317. |
[12] |
S. Fucik, O. John and J. Necas, On the existence of Schauder basis in Sobolev spaces, Comment. Math. Univ. Carolin, 13 (1972), 163-175. |
[13] |
T. Gallouet and R. Herbin, Existence of a solution to a coupled elliptic system, Appl.Math. Letters, 7 (1994), 49-55.
doi: 10.1016/0893-9659(94)90030-2. |
[14] |
C. Ogabi, On a class of nonlinear elliptic, anisotropic singular perturbations problems,, \textit{Preprint:} \url{https://hal.archives-ouvertes.fr/hal-01074262}., ().
|
[15] |
J. Serrin, Pathological solutions of elliptic differential equations, Ann. Sc. Norm. Sup. Pisa, 18 (1964), 385-387. |
show all references
References:
[1] |
R.A. Adams and John J.F. Fournier, Sobolev Spaces, Pure and Applied Mathematics, Academic Press, 2003. |
[2] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math, 12 (1959), 623-727. |
[3] |
L. Boccardo, T. Gallouët and J.L. Vazquez, Nonlinear elliptic equations in $R^n$ without growth restrictions on the data, Journal of Differential Equations, 105 (1993), 334-363.
doi: 10.1006/jdeq.1993.1092. |
[4] |
Ph. Bénilan, Philippe, L. Boccardo, Th. Gallouët, R. Gariepy, M. Pierre and J.L. Vazquez, An $L^{1}$-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola. Norm. Sup. Pisa Cl. Sci, 22 (1995), 241-273. |
[5] |
M. Chipot, Elliptic Equations, An Introductory Cours, Birkhauser, ISBN: 978-3764399818, 2009.
doi: 10.1007/978-3-7643-9982-5. |
[6] |
M. Chipot, On some anisotropic singular perturbation problems, Asymptotic Analysis, 55 (2007), 125-144. |
[7] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Acad. Sci. Paris, Ser. I, 346 (2008), 21-26.
doi: 10.1016/j.crma.2007.12.004. |
[8] |
M. Chipot and S. Guesmia, On the asymptotic behaviour of elliptic, anisotropic singular perturbations problems, Com. Pur. App. Ana, 8 (2009), 179-193.
doi: 10.3934/cpaa.2009.8.179. |
[9] |
M. Chipot, S. Guesmia and M. Sengouga, Singular perturbations of some nonlinear problems, J. Math. Sci, 176 2011, 828-843.
doi: 10.1007/s10958-011-0439-y. |
[10] |
M. Chipot and S. Guesmia, On a class of integro-differential problems, Commun. Pure Appl. Anal., 9 2010, 1249-1262.
doi: 10.3934/cpaa.2010.9.1249. |
[11] |
P. Enflo, A counterexample to the approximation problem in Banach spaces, Acta Mathematica, 130 (1973), 309-317. |
[12] |
S. Fucik, O. John and J. Necas, On the existence of Schauder basis in Sobolev spaces, Comment. Math. Univ. Carolin, 13 (1972), 163-175. |
[13] |
T. Gallouet and R. Herbin, Existence of a solution to a coupled elliptic system, Appl.Math. Letters, 7 (1994), 49-55.
doi: 10.1016/0893-9659(94)90030-2. |
[14] |
C. Ogabi, On a class of nonlinear elliptic, anisotropic singular perturbations problems,, \textit{Preprint:} \url{https://hal.archives-ouvertes.fr/hal-01074262}., ().
|
[15] |
J. Serrin, Pathological solutions of elliptic differential equations, Ann. Sc. Norm. Sup. Pisa, 18 (1964), 385-387. |
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