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On some variational problems set on domains tending to infinity
1. | Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich |
2. | Helmut Schmidt University / University of the Federal Armed Forces Hamburg, Department of Mechanical Engineering, Holstenhofweg 85, 22043, Hamburg, Germany |
3. | Tata Institute of Fundamental Research- CAM, Sharadanagar, GKVK Campus, Postbox - 560065, Bangalore, India |
References:
[1] |
J. Borwein, A. J. Guirao, P. Hajek and J. Vanderwerff, Uniformly convex functions on Banach spaces, Proc. Amer. Math. Soc., 137 (2009), 1081-1091.
doi: 10.1090/S0002-9939-08-09630-5. |
[2] |
P. G. Ciarlet, Introduction to Linear Shell Theory, Series in Applied Mathematics, (North-Holland, Amsterdam,) 1, 1998. |
[3] |
M. Chipot, $l$ Goes to Plus Infinity, Birkhäuser, 2002.
doi: 10.1007/978-3-0348-8173-9. |
[4] | |
[5] |
M. Chipot and S. Mardare, Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, J. Math. Pures Appl., 90 (2013), 133-159.
doi: 10.1016/j.matpur.2008.04.002. |
[6] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math., 4 (2002), 15-44.
doi: 10.1142/S0219199702000555. |
[7] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the eigenmodes for elliptic problems in domain becoming unbounded, Trans. AMS, 360 (2008), 3579-3602.
doi: 10.1090/S0002-9947-08-04361-4. |
[8] |
M. Chipot and A. Rougirel, Remarks on the asymptotic behaviour of the solution to parabolic problems in domains becoming unbounded, Nonlinear Analysis, 47 (2001), 3-11.
doi: 10.1016/S0362-546X(01)00151-1. |
[9] |
M. Chipot, P. Roy and I. Shafrir, Asymptotics of eigenstates of elliptic problems with mixed boundary data on domains tending to infinity, Asymptotic Analysis, 85 (2013), 199-227. |
[10] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Math. Acad. Sci., Paris, 346 (2008), 21-26.
doi: 10.1016/j.crma.2007.12.004. |
[11] |
M. Chipot and K. Yeressian, On the asymptotic behavior of variational inequalities set in cylinders, Discrete Contin. Dyn. Syst., 33 (2013), 4875-4890.
doi: 10.3934/dcds.2013.33.4875. |
[12] |
M. Chipot and K. Yeressian, Asymptotic behaviour of the solution to variational inequalities with joint constraints on its value and its gradient, Contemporary Mathematics, 594 (2013), 137-154.
doi: 10.1090/conm/594/11797. |
[13] |
M. Chipot and Y. Xie, On the asymptotic behaviour of the p-Laplace equation in cylinders becoming unbounded, Nonlinear partial differential equations and their applications, GAKUTO Internat. Ser. Math. Sci. Appl., Gakkotosho, Tokyo, 20 (2004), 16-27. |
[14] |
I. Chowdhury and P. Roy, On the asymptotic analysis of problems involving fractional laplacian in cylindrical domains tending to infinity,, preprint, ().
|
[15] |
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland Publishing Co., New York, 1976. |
[16] |
L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, 19, AMS, 1998. |
[17] |
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992. |
[18] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1983.
doi: 10.1007/978-3-642-61798-0. |
[19] |
S. Guesmia, Some convergence results for quasilinear parabolic boundary value problems in cylindrical domains of large size, Nonlinear Anal., 70 (2009), 3320-3331.
doi: 10.1016/j.na.2008.04.036. |
[20] |
S. Guesmia, Some results on the asymptotic behaviour for hyperbolic problems in cylindrical domains becoming unbounded, J. Math. Anal. Appl., 341 (2008), 1190-1212.
doi: 10.1016/j.jmaa.2007.11.001. |
show all references
References:
[1] |
J. Borwein, A. J. Guirao, P. Hajek and J. Vanderwerff, Uniformly convex functions on Banach spaces, Proc. Amer. Math. Soc., 137 (2009), 1081-1091.
doi: 10.1090/S0002-9939-08-09630-5. |
[2] |
P. G. Ciarlet, Introduction to Linear Shell Theory, Series in Applied Mathematics, (North-Holland, Amsterdam,) 1, 1998. |
[3] |
M. Chipot, $l$ Goes to Plus Infinity, Birkhäuser, 2002.
doi: 10.1007/978-3-0348-8173-9. |
[4] | |
[5] |
M. Chipot and S. Mardare, Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, J. Math. Pures Appl., 90 (2013), 133-159.
doi: 10.1016/j.matpur.2008.04.002. |
[6] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math., 4 (2002), 15-44.
doi: 10.1142/S0219199702000555. |
[7] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the eigenmodes for elliptic problems in domain becoming unbounded, Trans. AMS, 360 (2008), 3579-3602.
doi: 10.1090/S0002-9947-08-04361-4. |
[8] |
M. Chipot and A. Rougirel, Remarks on the asymptotic behaviour of the solution to parabolic problems in domains becoming unbounded, Nonlinear Analysis, 47 (2001), 3-11.
doi: 10.1016/S0362-546X(01)00151-1. |
[9] |
M. Chipot, P. Roy and I. Shafrir, Asymptotics of eigenstates of elliptic problems with mixed boundary data on domains tending to infinity, Asymptotic Analysis, 85 (2013), 199-227. |
[10] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Math. Acad. Sci., Paris, 346 (2008), 21-26.
doi: 10.1016/j.crma.2007.12.004. |
[11] |
M. Chipot and K. Yeressian, On the asymptotic behavior of variational inequalities set in cylinders, Discrete Contin. Dyn. Syst., 33 (2013), 4875-4890.
doi: 10.3934/dcds.2013.33.4875. |
[12] |
M. Chipot and K. Yeressian, Asymptotic behaviour of the solution to variational inequalities with joint constraints on its value and its gradient, Contemporary Mathematics, 594 (2013), 137-154.
doi: 10.1090/conm/594/11797. |
[13] |
M. Chipot and Y. Xie, On the asymptotic behaviour of the p-Laplace equation in cylinders becoming unbounded, Nonlinear partial differential equations and their applications, GAKUTO Internat. Ser. Math. Sci. Appl., Gakkotosho, Tokyo, 20 (2004), 16-27. |
[14] |
I. Chowdhury and P. Roy, On the asymptotic analysis of problems involving fractional laplacian in cylindrical domains tending to infinity,, preprint, ().
|
[15] |
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland Publishing Co., New York, 1976. |
[16] |
L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, 19, AMS, 1998. |
[17] |
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992. |
[18] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1983.
doi: 10.1007/978-3-642-61798-0. |
[19] |
S. Guesmia, Some convergence results for quasilinear parabolic boundary value problems in cylindrical domains of large size, Nonlinear Anal., 70 (2009), 3320-3331.
doi: 10.1016/j.na.2008.04.036. |
[20] |
S. Guesmia, Some results on the asymptotic behaviour for hyperbolic problems in cylindrical domains becoming unbounded, J. Math. Anal. Appl., 341 (2008), 1190-1212.
doi: 10.1016/j.jmaa.2007.11.001. |
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