Optimal Regularity and Nondegeneracy of a Free Boundary Problem Related to the Fractional Laplacian

Archive for Rational Mechanics and Analysis volume 208, pages 693–723 (2013)Cite this article

Abstract

We discuss the optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of Caffarelli et al. (J Eur Math Soc (JEMS) 12(5):1151–1179, 2010). A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be zero along the boundary.

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  1. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Ray Yang

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  1. Ray Yang
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Correspondence to Ray Yang.

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Communicated by F. Lin

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Yang, R. Optimal Regularity and Nondegeneracy of a Free Boundary Problem Related to the Fractional Laplacian. Arch Rational Mech Anal 208, 693–723 (2013). https://doi.org/10.1007/s00205-013-0619-7

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Keywords

  • Free Boundary
  • Free Boundary Problem
  • Harnack Inequality
  • Obstacle Problem
  • Poisson Kernel