CONTACT OF A THIN FREE BOUNDARY WITH A FIXED ONE IN THE SIGNORINI PROBLEM

Abstract. We study the Signorini problem near a fixed boundary, where the solution is “clamped down ” or “glued. ” We show that in general the solutions are at least C1/2 regular and that this regularity is sharp. We prove that near the actual points of contact of the free boundary with the fixed one the blowup solutions must have homogeneity κ ≥ 3/2, while at the non-contact points the homogeneity must take one of the values: 1/2, 3/2,..., m − 1/2,...