C∞ Regularity for the free boundary of one-phase Fractional Laplacian problem
Abstract
We consider a one-phase free boundary problem involving fractional Laplacian (-)s, 0<s<1. D. De Silva, O. Savin, and Y. Sire proved that the flat boundaries are C1,α. We raise the regularity to C∞, extending the result known for (-)1/2 by D. De Silva and O. Savin.
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