Abstract
AbstractWe address the question of finding global solutions of the Helmholtz equation that are positive in a given set. This question arises in inverse scattering for penetrable obstacles. In particular, we show that there are solutions that are positive on the boundary of a bounded Lipschitz domain.
Funder
Royal Institute of Technology
Publisher
Springer Science and Business Media LLC
Reference15 articles.
1. Bergh, J., Löfström, J.: Interpolation Spaces. An Introduction. Grundlehren der Mathematischen Wissenschaften, vol. 223. Springer-Verlag, Berlin, Heidelberg (1976)
2. Cakoni, F., Vogelius, M.S.: Singularities almost always scatter: Regularity results for non-scattering inhomogeneities. arXiv:2104.05058 (2021)
3. Chavel, I.: Isoperimetric Inequalities. Differential Geometric and Analytic Perspectives. Cambridge Tracts in Mathematics, vol. 145. Cambridge University Press, Cambridge (2001)
4. Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 4th edn. Applied Mathematical Sciences, vol. 93. Springer, Cham (2019)
5. Cronwell, R.H., Fox, R.H.: Introduction to Knot Theory. Graduate Text in Mathematics, vol. 57. Springer-Verlag, New York, Heidelberg (1977)
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