Recovery of discontinuous Lamé parameters from exterior Cauchy data. Issue 4 (11th May 2021)

• Record Type: Journal Article
• Authors: Caday, Peter; de Hoop, Maarten V.; Katsnelson, Vitaly; Uhlmann, Gunther
• Is Part Of: Communications in partial differential equations. Volume 46:Issue 4(2021)
• Page Start: 680
• Page End: 715
• Publication Date: 2021-05-11
• Subjects: Elastic wave equation -- inverse problems -- microlocal analysis; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2020.1857399
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: Consider an isotropic elastic medium Ω ⊂ R 3 whose Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only outside Ω and only for initial data supported outside Ω. Using the recently introduced scattering control series in the acoustic case, we prove that piecewise smooth Lamé parameters are uniquely determined by this map under certain geometric conditions.