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

Abstract

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.

arXiv comment50 pages

References in corpus (3)

• Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena
• On positivity sets for Helmholtz solutions
• Complete classification of global solutions to the obstacle problem

Cited by in corpus (2)

• Multi-phase $k$-quadrature domains and applications to acoustic waves and magnetic fields
• Multiphase quadrature domains (existence and uniqueness)