A stability result for a discontinuity jump inverse problem on linear elasticity equation

Abstract This article studies the inverse problem of determining the discontinuity jump of the displacement field, subject to a steady linear elasticity equation, on an interface from boundary measurements of displacements and tractions on boundary subdomains located on different sides of the interface. As a partial result, a conditional stability result of the discontinuity jump through internal measurements of the displacements is established. A conditional stability result for the discontinuity jump from boundary measurements is derived by a domain extension. Finally, an optimal control problem is presented to recover a tangential discontinuity jump, together with a numerical experiment to illustrate the theoretical findings.