Random homogenization of fractional obstacle problems

Luis Caffarelli; Antoine Mellet

doi:10.3934/nhm.2008.3.523

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2008, Volume 3, Issue 3: 523-554. Doi: 10.3934/nhm.2008.3.523

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Random homogenization of fractional obstacle problems

Luis Caffarelli^1, and
Antoine Mellet^2,

1.
Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082
2.
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2

Received: January 2008

Published: September 2008

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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.

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Mathematics Subject Classification: Primary: 74Q05; Secondary: 35R35.

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