Optimal Regularity of Lower-Dimensional Obstacle Problems

Journal of Mathematical Sciences volume 132, pages 274–284 (2006)Cite this 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.

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Author information

Affiliations

  1. Department of Applied Mathematics, University of Crete, Greece

    I. Athanasopoulos

  2. Department of Mathematics, University of Texas at Austine, USA

    L. A. Caffarelli

Authors
  1. I. Athanasopoulos
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  2. L. A. Caffarelli
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Additional information

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.

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Athanasopoulos, I., Caffarelli, L.A. Optimal Regularity of Lower-Dimensional Obstacle Problems. J Math Sci 132, 274–284 (2006). https://doi.org/10.1007/s10958-005-0496-1

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Keywords

  • Weighted Average
  • Space Dimension
  • Local Energy
  • Main Ingredient
  • Normal Derivative