Search results for " 35R35"

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A minimization problem with free boundary and its application to inverse scattering problems

2023

We study a minimization problem with free boundary, resulting in hybrid quadrature domains for the Helmholtz equation, as well as some application to inverse scattering problem.

Mathematics - Analysis of PDEsFOS: MathematicsAnalysis of PDEs (math.AP)35J05 35J15 35J20 35R30 35R35
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Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena

2022

In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering problems, and show that there are non-scattering domains for the Helmholtz equation at any positive frequency that have inward cusps.

metaharmonic functionsmatematiikkapartial balayageyhtälötmean value theoremMathematics::Numerical Analysis35J05 35J15 35J20 35R30 35R35quadrature domainnon-scattering phenomenaMathematics - Analysis of PDEsFOS: MathematicsHelmholtz equationacoustic equationAnalysisAnalysis of PDEs (math.AP)
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