6533b7cefe1ef96bd1257a73
RESEARCH PRODUCT
Free boundary methods and non-scattering phenomena
Mikko SaloHenrik Shahgholiansubject
FOS: Physical sciencesBoundary (topology)01 natural sciencesinversio-ongelmatTheoretical Computer ScienceMathematics - Analysis of PDEsMathematics (miscellaneous)ConverseFOS: MathematicsPoint (geometry)0101 mathematicsMathematical PhysicsComplement (set theory)MathematicsosittaisdifferentiaaliyhtälötQuadrature domainsScatteringApplied MathematicsResearch010102 general mathematicsMathematical analysisMathematical Physics (math-ph)010101 applied mathematicsComputational MathematicsObstacleInverse scattering problemAnalysis of PDEs (math.AP)description
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point. These facts are proved by invoking results from the theory of free boundary problems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-01-01 | Research in the Mathematical Sciences |