Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Mantile, Andrea¹  Posilicano, Andrea²  Sini, Mourad³ 

[1] Univ Reims, Lab Math, CNRS, FR3399, Moulin Housse BP 1039, F-51687 Reims, France

[2] Univ Insubria, DiSAT, Sez Matemat, Via Valleggio 11, I-22100 Como, Italy

[3] Austrian Acad Sci, RICAM, Altenbergerstr 69, A-4040 Linz, Austria

关键词: Inverse scattering;    Acoustic equation;    Schrodinger operators;   

DOI  :  10.1016/j.jde.2018.05.029

来源: Elsevier

【 摘 要 】

We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across Sigma subset of Gamma = partial derivative Omega, where Omega is a bounded open subset of R-3 with a Lipschitz boundary. This follows from a uniqueness result in inverse scattering for Schrodinger operators with singular delta-type potential supported on the surface Gamma and of strength alpha is an element of L-p (Gamma), p > 2. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free