Potential recovery for Reissner-Mindlin and Kirchhoff-Love plate models using global Carleman estimates (Q2861879)

In this paper the authors consider two linear plate models coming from linear elasticity: the Reissner-Mindlin (R-M) and Kirchhoff-Love (K-L) models; for these ones they deal with a particular inverse problem arising to determine the spatial dependence from boundary or internal measurements of a coefficient in the zero order term in linear plate equation. They consider this research as a first stage of the more complicated inverse problem related to the main coefficient in a linear plate equation. Because the mathematical analysis of the inverse problem is built on its stability analysis, studied using the global Carlemann estimates, the authors work is to obtain these inequalities for R-M and K-L models. For this purpose they study preliminarly some results of existence (by Galerkin method), uniqueness, regularity (using Gronwall inequality) for solutions of these systems. Moreover they prove some energy estimates. To obtain their result, the authors combine global Carlemann inequalities, after writing the system as a weakly coupled system of wave equations and then applying the approach of Bukhgeim-Klibanov. In this work, the authors, as consequence of their research, prove the existence, uniqueness and regularity of R-M solutions in the case when the Lamé coefficients depend on the space variable, generalizing the results obtained in the previous work.