Geodesic
Asymptotic solution of the~Signorini problem with an~obstacle on a~thin elongated set
Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1411-1442

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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. 
@article{SM_1996_187_10_a0,
     author = {I. I. Argatov and S. A. Nazarov},
     title = {Asymptotic solution of {the~Signorini} problem with an~obstacle on a~thin elongated set},
     journal = {Sbornik. Mathematics},
     pages = {1411--1442},
     publisher = {mathdoc},
     volume = {187},
     number = {10},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_10_a0/}
}
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I. I. Argatov; S. A. Nazarov. Asymptotic solution of the~Signorini problem with an~obstacle on a~thin elongated set. Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1411-1442. http://geodesic.mathdoc.fr/item/SM_1996_187_10_a0/