A free boundary approach to non-scattering obstacles with vanishing contrast
Analysis of PDEs
2025-06-30 v1
Abstract
Motivated by questions in inverse scattering theory, we develop free boundary methods in obstacle problems where both the solution and the right hand side of the equation may have varying sign. The key condition that prevents the appearance of corners is that the right hand side should be related to a harmonic polynomial. In this setting we prove new free boundary results not found in existing literature. Notably, our results imply that piecewise or convex penetrable obstacles in two dimensions and edge points in higher dimensions always cause nontrivial scattering of any incoming wave.
Keywords
Cite
@article{arxiv.2506.22328,
title = {A free boundary approach to non-scattering obstacles with vanishing contrast},
author = {Mikko Salo and Henrik Shahgholian},
journal= {arXiv preprint arXiv:2506.22328},
year = {2025}
}