An inverse problem for inhomogeneous Signorini obstacle

TL;DR

This paper addresses the inverse problem of uniquely identifying a Signorini obstacle's shape and properties from boundary measurements in scalar and elasticity contexts.

Contribution

It establishes the unique determination of the obstacle's shape and function from boundary data for the Signorini problem in both scalar and elastic cases.

Findings

Unique determination of obstacle shape from boundary measurements.

Applicability to both scalar and elasticity Signorini problems.

Boundary measurements suffice for obstacle reconstruction.

Abstract

This paper investigates the inverse problem of determining a general Signorini obstacle using boundary measurements. We demonstrate that both the shape of the obstacle and the obstacle function can be uniquely determined from solution measurements taken on an arbitrary open subset of the boundary. This result applies to both the scalar and elasticity versions of the Signorini problem.