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

Abstract

In this paper, we consider two linear plate models, namely the Reissner–Mindlin system (R–M) and the Kirchhoff–Love equation (K–L), which come from linear elasticity. We prove global Carleman inequalities for both models with boundary observations and under a suitable hypothesis on the parameters. We use these estimates to study the inverse problem of recovering a spatially dependent potential from knowledge of Neumann boundary data. We obtain L2-Lipschitz stability for K–L and H1-Lipschitz stability for R–M under the assumption that the potentials are equal at the boundary.