Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian
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boundaryproblemrelatedfractionalfreelaplaciannondegeneracyoptimal
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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, Roquejoffre, and Sire. A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be 0 along the boundary.
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