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Journal article
On corner scattering for operators of divergence form and applications to inverse scattering
Communications in partial differential equations, v 46(3), pp 413-441
11 Nov 2020
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Abstract
We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both "conductivity" in the divergence form and "potential" in the lower order term. The support of the inhomogeneity is assumed to contain a convex corner. We prove that, due to the presence of such corner under appropriate assumptions on the potential and conductivity in the vicinity of the corner, any incident field scatters. Based on corner scattering analysis we present a uniqueness result on determination of the polygonal convex hull of the support of admissible inhomogeneities, from scattering data corresponding to one single incident wave. These results require only certain regularity around the corner for the coefficients modeling the inhomogeneity, whereas away from the corner they can be quite general. Our main results on scattering and inverse scattering are established for
while some analytic tools are developed in any dimension
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Details
- Title
- On corner scattering for operators of divergence form and applications to inverse scattering
- Creators
- Fioralba Cakoni - Rutgers, The State University of New JerseyJingni Xiao - Rutgers, The State University of New Jersey
- Publication Details
- Communications in partial differential equations, v 46(3), pp 413-441
- Publisher
- Taylor & Francis
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000629811100001
- Scopus ID
- 2-s2.0-85103066222
- Other Identifier
- 991021878015504721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied