@article{SEDP_2006-2007____A13_0, author = {Robbiano, Luc and Zuily, Claude}, title = {Effet r\'egularisant pour les solutions de l{\textquoteright}\'equation de {Schr\"odinger} dans un domaine ext\'erieur}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:13}, pages = {1--10}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2006-2007}, mrnumber = {2385200}, language = {fr}, url = {http://archive.numdam.org/item/SEDP_2006-2007____A13_0/} }
TY - JOUR AU - Robbiano, Luc AU - Zuily, Claude TI - Effet régularisant pour les solutions de l’équation de Schrödinger dans un domaine extérieur JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:13 PY - 2006-2007 SP - 1 EP - 10 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_2006-2007____A13_0/ LA - fr ID - SEDP_2006-2007____A13_0 ER -
%0 Journal Article %A Robbiano, Luc %A Zuily, Claude %T Effet régularisant pour les solutions de l’équation de Schrödinger dans un domaine extérieur %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:13 %D 2006-2007 %P 1-10 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_2006-2007____A13_0/ %G fr %F SEDP_2006-2007____A13_0
Robbiano, Luc; Zuily, Claude. Effet régularisant pour les solutions de l’équation de Schrödinger dans un domaine extérieur. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Exposé no. 13, 10 p. http://archive.numdam.org/item/SEDP_2006-2007____A13_0/
[B1] Burq N. : Mesures semi classiques et mesures de défaut, Séminaire Bourbaki, Astéristique n245 (1997), p. 167-195. | EuDML | Numdam | MR | Zbl
[B2] Burq N. : Smoothing Effect for Schrödinger Boundary Value Problems, Duke Math. Journal 123 (2004), 403-427. | MR | Zbl
[B3] Burq N. : Semi-classical estimates for the resolvant in non trapping geometries, IMRN n5 (2002), p. 221-241. | MR | Zbl
[B-G] Burq N., Gérard P. : Condition nécessaire et suffisante pour la controlabilité exacte des ondes, CRAS 325 (1997), 749-752. | MR | Zbl
[C-S] Constantin, P., Saut, J-C. : Local smoothing properties of dispersive equations, Journal American Mathematical Society (1988) 413-439. | MR | Zbl
[Da] Davies E.B., Spectral theory and differential operators, Cambridge studies in advanced mathematics, 42, Cambridge Univers. press | MR | Zbl
[D1] Doï, S. : Smoothing effects of Schrödinger evolution group on Riemannian manifolds, Duke Math. J. 82 (1996) 679-706. | MR | Zbl
[D2] Doï, S. : Smoothing effects for Schrödinger evolution equation and global behavior of geodesic flow, Math. Ann. 318 (2000) 355-389. | MR | Zbl
[D3] Doï, S. : Remarks on the Cauchy problem for Schrödinger type equations, Comm. in pde, 21 (1996) 163-178. | MR | Zbl
[D4] Doï, S. : Smoothness of solutions for Schrödinger equations with unbounded potential., Publ.Res.Inst.Math.Sci 41 (2005), 1, 175-221. | MR | Zbl
[G-L] Gérard P., Leichtnam E. : Ergodic properties of eigenfunctions for the Dirichlet problem, Duke Math. J. 71 n2 (1993), p. 559-607. | MR | Zbl
[Hö] Hörmander L. : The analysis of Linear Partial Differential Operators I, III, Springer Verlag, Berlin, Heidelberg, New-York (1985). | MR | Zbl
[K] Kato T. : On the Cauchy problem for the (generalized) KdV equation, Stud. Appl. Math. Adv. Math. Suppl. Stud. 8 (1983) 93-128. | MR | Zbl
[L] Lebeau G. : Équation des ondes amorties. Algebraic and Geometric methods in math. physics, Math. Phys. Math. Studies, vol. 19, Kluwer Acad. Publ. Dovdrecht (1996), p. 73-109. | MR | Zbl
[L-P] Lions P.L., Paul, T. : Sur les mesures de Wigner, Rev. Mat. Iberoamericana 9 (1993) 553-618 | MR | Zbl
[M-S] Melrose R.B., Sjöstrand J. : Singularities of boundary value problems I, Comm. Pure Appl. Math 31 n 5 (1978), 593-617. | MR | Zbl
[Mi] Miller L. : Refraction of high-frequency waves density by sharp interfaces and semi classical measures at the boundary, J. Math. Pures Appl. (9) 79 n 3 (2000), p. 227-269. | MR | Zbl
[R-Z] Robbiano L., Zuily C. : Remark on the Kato smoothing effect for Schrödinger equation with superquadratic potentials Preprint.
[S] Sjölin P. : Regularity of solution to the Schrödinger equation, Duke Math. J. 55 (1987) 699-715. | MR | Zbl
[T] Tartar, Luc : Memory effects and homogenization Arch. Rational Mech. Anal. 111 (1990) 121-133. | MR | Zbl
[V] Vega L. : Schrödinger equations, pointwise convergence to the initial data, Proc. Amer. Math. Soc. 102 (1988) 874-878. | MR | Zbl
[Y] Yajima K. : On smoothing property of Schrödinger propagator, Lectures notes in Math. 1450 Springer Verlag (1990) 20-35. | MR | Zbl
[Y-Z1] Yajima K., Zhang G.P. : Smoothing property for Schrödinger equations with potential super-quadratic at infinity, Comm. Math. Phys. 221 (2001) 573-590. | MR | Zbl
[Y-Z2] Yajima K., Zhang G.P. : Local smoothing property and Strichartz inequality for Schrödinger equations with potential superquadratic at infinity, Journ. Diff. Equ. 202 (2004) 81-110. | MR | Zbl