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

The Signorini problem for a Poisson equation is studied subject to onesided constraints imposed on a narrow annular boundary band $\Gamma _\varepsilon$ (of width $O(\varepsilon )$). An asymptotic analysis yields a resultant variational inequality on the contour $\Gamma$ to which $\Gamma _\varepsilon$ contracts as $\varepsilon \to 0$. 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.