Optimal Regularity of Lower-Dimensional Obstacle Problems
- Cite this article as:
- Athanasopoulos, I. & Caffarelli, L.A. J Math Sci (2006) 132: 274. doi:10.1007/s10958-005-0496-1
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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.