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The Structure of the Free Boundary for Lower Dimensional Obstacle Problems

From: American Journal of Mathematics
Volume 130, Number 2, April 2008
pp. 485-498 | 10.1353/ajm.2008.0016

Abstract

Abstract:

We study the regularity of the "free surface" in boundary obstacle problems. We show that near a non-degenerate point the free boundary is a C1,α (n - 2)-dimensional surface in Rn-1.