Global stability for an inverse problem in soil-structure interaction

An important issue in structural building design is the soil–structure interaction. We make reference to the Winkler model and consider the inverse problem of determining the Winkler subgrade reaction coefficient k(x) of a slab foundation modelled as a thin elastic plate clamped at the boundary and loaded by a concentrated force. We investigate whether the coefficient k(x) depends continuously on the transversal deflection taken at the interior points. We prove a global Hölder stability estimate under some reasonable regularity assumptions on the unknown Winkler coefficient.