scholarly journals On a Limiting Absorption Principle for Sesquilinear Forms with an Application to the Helmholtz Equation in a Waveguide

2020 ◽  
pp. 291-307
Author(s):  
Ben Schweizer ◽  
Maik Urban
Keyword(s):  
Helmholtz Equation ◽  
Limiting Absorption Principle ◽  
Sesquilinear Forms

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.

scholarly journals Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

2014 ◽  
Vol 144 (4) ◽  
pp. 857-890 ◽  
Author(s):  
Miren Zubeldia
Keyword(s):  
Helmholtz Equation ◽  
Unique Solution ◽  
A Priori ◽  
Radiation Condition ◽  
Singular Potentials ◽  
Absorption Method ◽  
Limiting Absorption Principle ◽  
Electric Potentials ◽  
Image Position

We study the Helmholtz equationin ℝd with magnetic and electric potentials that are singular at the origin and decay at ∞. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.

scholarly journals A limiting absorption principle for the Helmholtz equation with variable coefficients

2018 ◽  
Vol 8 (4) ◽  
pp. 1349-1392 ◽  
Author(s):  
Federico Cacciafesta ◽  
Piero D'Ancona ◽  
Renato Lucà
Keyword(s):  
Helmholtz Equation ◽  
Variable Coefficients ◽  
Limiting Absorption Principle

A preconditioned method for the solution of the Robbins problem for the Helmholtz equation

2011 ◽  
Vol 51 ◽  
pp. 87
Author(s):  
Jiang Le ◽  
Huang Jin ◽  
Xiao-Guang Lv ◽  
Qing-Song Cheng
Keyword(s):  
Helmholtz Equation
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