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Journal of Mathematical Sciences

, Volume 132, Issue 3, pp 274–284 | Cite as

Optimal Regularity of Lower-Dimensional Obstacle Problems

  • I. Athanasopoulos
  • L. A. Caffarelli
Article

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.

Keywords

Weighted Average Space Dimension Local Energy Main Ingredient Normal Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • I. Athanasopoulos
    • 1
  • L. A. Caffarelli
    • 2
  1. 1.Department of Applied MathematicsUniversity of CreteGreece
  2. 2.Department of MathematicsUniversity of Texas at AustineUSA

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