Networks and Heterogeneous Media (NHM)

Random homogenization of fractional obstacle problems

Pages: 523 - 554, Volume 3, Issue 3, September 2008      doi:10.3934/nhm.2008.3.523

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Luis Caffarelli - Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082, United States (email)
Antoine Mellet - Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada (email)

Abstract: We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.

Keywords:  Homogenization, Obstacle Problem, Fractional Laplace
Mathematics Subject Classification:  Primary: 74Q05; Secondary: 35R35.

Received: January 2008;      Available Online: March 2008.