The forward problem for the electromagnetic Helmholtz equation with critical singularities

被引：17

作者：

Antonio Barcelo, Juan ^{[1
]}

Vega, Luis ^{[2
]}

Zubeldia, Miren ^{[2
]}

机构：

[1] Univ Politecn Madrid, ETSI Caminos, E-28040 Madrid, Spain

[2] Univ Basque Country, Dept Matemat, E-48080 Bilbao, Spain

来源：

ADVANCES IN MATHEMATICS | 2013年 / 240卷

基金：

欧洲研究理事会;

关键词：

Singular potentials; Magnetic Schrodinger operator; Uniform estimates; Cross-section; Spectral theory; LONG-RANGE POTENTIALS; SCHRODINGER-OPERATORS; SCATTERING-THEORY; DIFFERENTIAL-OPERATORS; INEQUALITIES; DECAY; WAVE;

D O I：

10.1016/j.aim.2013.03.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the forward problem of the magnetic Schrodinger operator with potentials that have a strong singularity at the origin. We obtain new resolvent estimates and give some applications on the spectral measure and on the solutions of the associated evolution problem. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：636 / 671

页数：36

共 51 条

[1] ASYMPTOTIC PROPERTIES OF SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH SIMPLE CHARACTERISTICS [J].

AGMON, S ;

HORMANDER, L .

JOURNAL D ANALYSE MATHEMATIQUE, 1976, 30 :1-38

[2]

Agmon S., 1975, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, V2, P151

[3] Some special solutions of the Schrodinger equation [J].

Barcelo, J. A. ;

Bennett, J. M. ;

Carbery, A. ;

Ruiz, A. ;

Vilela, M. C. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2007, 56 (04) :1581-1593

[4] Weak Dispersive Estimates for Schrodinger Equations with Long Range Potentials [J].

Barcelo, J. A. ;

Ruiz, A. ;

Vega, L. ;

Vilela, M. C. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (01) :74-105

[5] Spherical perturbations of Schrodinger equations [J].

Barceló, JA ;

Bennett, JM ;

Ruiz, A .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2006, 12 (03) :269-290

[6] Some dispersive estimates for Schrodinger equations with repulsive potentials [J].

Barcelo, Juan A. ;

Ruiz, Alberto ;

Vega, Luis .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 236 (01) :1-24

[7]

Burq N, 2004, INDIANA U MATH J, V53, P1665

[8] Strichartz estimates for the wave and Schrodinger equations with the inverse-square potential [J].

Burq, N ;

Planchon, F ;

Stalker, JG ;

Tahvildar-Zadeh, AS .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 203 (02) :519-549

[9]

Cycon H. L., 1987, SCRODINGER OPERATORS

[10] Endpoint Strichartz estimates for the magnetic Schrodinger equation [J].

D'Ancona, Piero ;

Fanelli, Luca ;

Vega, Luis ;

Visciglia, Nicola .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (10) :3227-3240

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