Steady-state scattering theory in exterior domains and the limiting absorption principle

1975 ◽  
pp. 49-75
Author(s):  
Calvin H. Wilcox
Keyword(s):  
Steady State ◽  
Scattering Theory ◽  
Exterior Domains ◽  
Limiting Absorption Principle

On the limiting absorption and amplitude principles for transmission problems with unbounded interfaces

1997 ◽  
Vol 122 (2) ◽  
pp. 343-356
Author(s):  
BO ZHANG
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Resolvent Estimate ◽  
State Problem ◽  
Limiting Absorption Principle ◽  
Low Frequencies ◽  
State Operator ◽  
Second Order Differential Equations ◽  
Transmission Problems ◽  
Steady State Problem

We consider the transmission problem for second-order differential equations with unbounded interfaces. The spaces B and B* are used to prove the limiting absorption principle for the steady-state problem and to establish the resolvent estimate at low frequencies for the steady-state operator. These are then applied in showing the validity of the limiting amplitude principle for such an operator.

scholarly journals Steady-state current transfer and scattering theory

2010 ◽  
Vol 133 (5) ◽  
pp. 054105 ◽  
Author(s):  
Vered Ben-Moshe ◽  
Dhurba Rai ◽  
Spiros S. Skourtis ◽  
Abraham Nitzan
Keyword(s):  
Steady State ◽  
Scattering Theory ◽  
Current Transfer ◽  
Steady State Current

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

2013 ◽  
Vol 143 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Juan Antonio Barceló ◽  
Luca Fanelli ◽  
Alberto Ruiz ◽  
Maricruz Vilela
Keyword(s):  
Helmholtz Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Exterior Domains ◽  
Limiting Absorption Principle ◽  
Electromagnetic Potentials ◽  
Priori Estimates ◽  
Embedded Eigenvalues

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.

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