Overdetermined Boundary Value Problems, Quadrature Domains and Applications

2005 ◽  
Vol 5 (1) ◽  
pp. 19-48 ◽  
Author(s):  
Dmitry Khavinson ◽  
Alexander Yu. Solynin ◽  
Dimiter Vassilev
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Quadrature Domains

scholarly journals Free boundary methods and non-scattering phenomena

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Mikko Salo ◽  
Henrik Shahgholian
Keyword(s):  
Free Boundary ◽  
Incident Wave ◽  
Scattering Theory ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Quadrature Domains ◽  
Real Analytic ◽  
Boundary Methods ◽  
Inverse Scattering Theory ◽  
Zero Frequency

AbstractWe 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.

scholarly journals Szegö Coordinates, Quadrature Domains, and Double Quadrature Domains

2010 ◽  
Vol 11 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Steven R. Bell ◽  
Björn Gustafsson ◽  
Zachary A. Sylvan
Keyword(s):  
Quadrature Domains
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