, Volume 132, Issue 3, pp 274-284

Optimal Regularity of Lower-Dimensional Obstacle Problems

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Abstract

In this paper, we prove that solutions to the “boundary obstacle problem” have the optimal regularity, C1,1/2, in any space dimension. This bound depends only on the local L2-norm of the solution. Main ingredients in the proof are the quasiconvexity of the solution and a monotonicity formula for an appropriate weighted average of the local energy of the normal derivative of the solution. Bibliography: 8 titles.

Dedicated to Nina Nikolaevna Uraltseva on the occasion of her 70th birthday
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 49–66.