Smoothing effect for Schrodinger boundary value problems

被引：65

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

收藏

页码：403 / 427

页数：25

相关论文

共 30 条

[1] Regularity and decay of solutions to the stark evolution equation [J].

Ben-Artzi, M ;

Devinatz, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 154 (02) :501-512

[2] DECAY AND REGULARITY FOR THE SCHRODINGER-EQUATION [J].

BENARTZI, M ;

KLAINERMAN, S .

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 [J].

Burq, N .

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 [J].

Burq, N ;

Lebeau, G .

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 [J].

Burq, N ;

Gerard, P .

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 [J].

CONSTANTIN, P ;

SAUT, JC .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1989, 38 (03) :791-810

[10]

Doi S, 1996, COMMUN PART DIFF EQ, V21, P163