The Linearized Inverse Boundary Value Problem in Strain Gradient Elasticity

ABSTRACT In this paper we study the linearized version of the strain gradient elasticity equation in with constant coefficients and we prove that one can determine the two Lamé coefficients as well as the internal strain gradient parameter , as indicated by Mindlin in his revolutionary papers in 1963–1965, by boundary measurements. This is accomplished via the investigation of the corresponding Steklov‐Poincaré operator, which, in the current situation, stems from a fourth order boundary value problem and merits several qualitative differences in comparison to the classical elasticity problem. The investigation of the Fréchet derivative of this operator is the cornerstone in the realm of the solvability of the inverse problem.