A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains

被引：8

作者：

Antonio Barcelo, Juan ^{[1
]}

Fanelli, Luca ^{[2
]}

Ruiz, Alberto ^{[3
]}

Vilela, Maricruz ^{[4
]}

机构：

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

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

[3] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[4] Univ Valladolid, Dept Matemat Aplicada, Segovia, Spain

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2013年 / 143卷 / 01期

关键词：

SCHRODINGER-OPERATORS; DECAY;

D O I：

10.1017/S0308210511000850

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension n >= 3. Using multiplier techniques in the style of Morawetz, we prove a family of a priori estimates from which the limiting absorption principle follows. Moreover, we give some standard applications to cases with an absence of embedded eigenvalues and zero resonances, under explicit conditions on the potentials.

引用

页码：1 / 19

页数：19

共 28 条

[1]

Agmon S., 1975, J ANAL MATH, V30, P1

[2]

Agmon S., 1975, ANN SC NORM SUP PI 4, V2, P121

[3]

AGMON S, 1990, ANAL CETERA, P39

[4]

ALBER HD, 1983, J REINE ANGEW MATH, V345, P39

[5]

[Anonymous], OSAKA J MATH

[6]

Arai M., 1972, PUBL RIMS, V7, P621

[7] 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

[8] Weighted estimates for the Helmholtz equation and some applications [J].

Barcelo, JA ;

Ruiz, A ;

Vega, L .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 150 (02) :356-382

[9] 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

[10]

Cycon H.L., 1987, TEXTS MONOGRAPHS PHY

← 1 2 3 →