Journal of Mathematical Sciences

, Volume 132, Issue 3, pp 274–284

Optimal Regularity of Lower-Dimensional Obstacle Problems

  • I. Athanasopoulos
  • L. A. Caffarelli

DOI: 10.1007/s10958-005-0496-1

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


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.

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

Personalised recommendations