@article{AIHPC_2004__21_3_295_0, author = {Burq, Nicolas and G\'erard, P and Tzvetkov, N}, title = {On nonlinear Schr\"odinger equations in exterior domains}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {21}, year = {2004}, pages = {295-318}, doi = {10.1016/j.anihpc.2003.03.002}, mrnumber = {2068304}, zbl = {1061.35126}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_3_295_0} }
Burq, N; Gérard, P; Tzvetkov, N. On nonlinear Schrödinger equations in exterior domains. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 295-318. doi : 10.1016/j.anihpc.2003.03.002. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_3_295_0/
[1] Decay and regularity for the Schrödinger equation, J. Anal. Math. 58 (1992) 25-37. | MR 1226935 | Zbl 0802.35057
, ,[2] Interpolation Spaces, Springer-Verlag, 1976. | Zbl 0344.46071
, ,[3] Global Solutions of Nonlinear Schrödinger Equations, Colloq. Publications, American Math. Soc, 1999. | MR 1691575 | Zbl 0933.35178
,[4] Problems in Hamiltonian PDE's. GAFA 2000 (Tel Aviv, 1999), Geom. Funct. Anal. (Special Volume, Part I) (2000) 32-56. | MR 1826248 | Zbl 1050.35016
,[5] Nonlinear Schrödinger evolution equations, Nonlinear Anal. 4 (1980) 677-681. | MR 582536 | Zbl 0451.35023
, ,[6] Contrôle de l'équation des ondes dans des ouverts peu réguliers, Asymptotic Anal. 14 (1997) 157-191. | MR 1451210 | Zbl 0892.93009
,[7] Décroissance de l'énergie locale de l'équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel, Acta Math. 180 (1998) 1-29. | MR 1618254 | Zbl 0918.35081
,[8] Semi-classical estimates for the resolvent in nontrapping geometries, Internat. Math. Res. Notices (2002) 221-241. | MR 1876933 | Zbl 01719337
,[9] N. Burq, P. Gérard, N. Tzvetkov, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, Amer. J. Math., in press. | MR 2058384 | Zbl 1067.58027
[10] The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold, Proceedings of the Öresund Symposium on Partial Differential Equations, Lund, May 23-25, 2002, J. Nonlinear Math. Phys. 10 (2003) 12-27, Supplement 1. | MR 2063542
, , ,[11] Two singular dynamics of the nonlinear Schrödinger equation on a plane domain, Geom. Funct. Anal. 13 (2003) 1-19. | MR 1978490 | Zbl 1044.35084
, , ,[12] An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains, in: , (Eds.), Proceedings of the Conference on Hyperbolic PDEs and Related Topics, Cortona, 2002, submitted for publication. | MR 2056842 | Zbl 02072521
, , ,[13] An introduction to nonlinear Schrödinger equations, second ed., Textos de Métodos Matemáticos 26 (1993).
,[14] Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988) 413-439. | MR 928265 | Zbl 0667.35061
, ,[15] Local smoothing properties of Schrödinger equations, Indiana Univ. Math. J. 38 (1989) 791-810. | MR 1017334 | Zbl 0712.35022
, ,[16] Maximal functions associated to filtrations, J. Funct. Anal. 179 (2001) 409-425. | MR 1809116 | Zbl 0974.47025
, ,[17] Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math. J. 82 (1996) 679-706. | MR 1387689 | Zbl 0870.58101
,[18] On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 46 (1987) 113-129. | Numdam | MR 877998 | Zbl 0632.35038
,[19] A remark on the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, Trans. Amer. Math. Soc. 299 (1987) 193-203. | MR 869407 | Zbl 0638.35043
,[20] S. Keraani, Étude de quelques régimes asymptotiques de l'équation de Schrödinger, PhD Thesis, Université de Paris-Sud, December 2000.
[21] Scattering Theory, Pure Appl. Math., vol. 26, Academic Press, 1989. | MR 1037774 | Zbl 0697.35004
, ,[22] Quelques méthodes de résolution des équations aux dérivées partielles non linéaires, Dunod, Paris, 1969. | Zbl 0189.40603
,[23] Singularities of boundary value problems I, Comm. Pure Appl. Math. 31 (1978) 593-617. | MR 492794 | Zbl 0368.35020
, ,[24] Singularities of boundary value problems II, Comm. Pure Appl. Math. 35 (1982) 129-168. | MR 644020 | Zbl 0546.35083
, ,[25] Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger equations, J. Math. Anal. Appl. 155 (1991) 531-540. | MR 1097298 | Zbl 0733.35095
, ,[26] Nonlinear semi-groups, Ann. Math. 78 (1963) 339-364. | MR 152908 | Zbl 0204.16004
,[27] The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Applied Mathematical Sciences, vol. 139, Springer-Verlag, New York, 1999. | MR 1696311 | Zbl 0928.35157
, ,[28] Regularity of solutions to Schrödinger equations, Duke Math. J. 55 (1987) 699-715. | MR 904948 | Zbl 0631.42010
,[29] On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc. 8 (1995) 879-916. | MR 1308407 | Zbl 0860.35081
, ,[30] Strichartz estimates for a Schrödinger operator with nonsmooth coefficients, Comm. Partial Differential Equations 27 (2002) 1337-1372. | MR 1924470 | Zbl 1010.35015
, ,[31] Partial Differential Equations, Applied Mathematical Sciences, vols. 115, 116, 117, Springer-Verlag, New York, 1996. | MR 1395147 | Zbl 0869.35003
,[32] On smooth solutions to the initial-boundary value problem for the nonlinear Schrödinger equation in two space dimensions, Nonlinear Anal. 13 (1989) 1051-1056. | MR 1013309 | Zbl 0693.35133
,[33] On global solutions to the initial-boundary value problem for the nonlinear Schrödinger equation in exterior domains, Comm. Partial Differential Equations 16 (1991) 885-907. | MR 1116848 | Zbl 0738.35093
,[34] Global solutions of the nonlinear Schrödinger equation in exterior domains, Comm. Partial Differential Equations 8 (1984) 1337-1374. | MR 711442 | Zbl 0542.35027
,[35] Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach, New York, 1988. | MR 1054376 | Zbl 0743.35001
,[36] Semiclassical estimates in asymptotically euclidean scattering, Comm. Math. Phys. 212 (2000) 205-217. | MR 1764368 | Zbl 0955.58023
, ,[37] Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988) 874-878. | MR 934859 | Zbl 0654.42014
,[38] On the solvability of mixed problem for a nonlinear equation of Schrödinger type, Soviet Math. Dokl. 29 (1984) 281-284. | Zbl 0585.35019
,