Asymptotic solution of the Signorini problem with an obstacle on a thin elongated set

Abstract

The Signorini problem for a Poisson equation is studied subject to onesided constraints imposed on a narrow annular boundary band (of width ). An asymptotic analysis yields a resultant variational inequality on the contour to which contracts as . Approximate solutions of the resultant inequality are derived with varying degree of accuracy and used to construct and justify an asymptotic solution of the original Signorini problem.