Smoothing effect for Schrodinger boundary value problems

被引：64

作者：

Burq, N ^{[1
]}

机构：

[1] Univ Paris 11, Dept Math, F-91405 Orsay, France

来源：

DUKE MATHEMATICAL JOURNAL | 2004年 / 123卷 / 02期

关键词：

D O I：

10.1215/S0012-7094-04-12326-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show the necessity of the nontrapping condition for the plain smoothing effect (H-1/2) for the Schrodinger equation with Dirichlet boundary conditions in exterior problems. We also give a class of trapped obstacles (Ikawa's example) for which we can prove a weak (H1/2-epsilon) smoothing effect.

引用

页码：403 / 427

页数：25

共 30 条

[1] Regularity and decay of solutions to the stark evolution equation
Ben-Artzi, M
Devinatz, A
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 154 (02) : 501 - 512
[2] DECAY AND REGULARITY FOR THE SCHRODINGER-EQUATION
BENARTZI, M
KLAINERMAN, S
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1992, 58 : 25 - 37
[3] Local energy decay of the wave equation for the exterior problem and absence of resonance in the neighborhood of the real axis
Burq, N
[J]. ACTA MATHEMATICA, 1998, 180 (01) : 1 - 29
[4] Burq N, 2002, INT MATH RES NOTICES, V2002, P221
[5] Microlocal defect measures, application to the Lame system
Burq, N
Lebeau, G
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2001, 34 (06): : 817 - 870
[6] Burq N, 1997, ASTERISQUE, P167
[7] A necessary and sufficient condition for the exact controllability of the wave equation
Burq, N
Gerard, P
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (07): : 749 - 752
[8] BURQ N, 2002, IN PRESS ANN I H POI
[9] LOCAL SMOOTHING PROPERTIES OF SCHRODINGER-EQUATIONS
CONSTANTIN, P
SAUT, JC
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1989, 38 (03) : 791 - 810
[10] Doi S, 1996, COMMUN PART DIFF EQ, V21, P163

← 1 2 3 →