Optimal Regularity and Nondegeneracy of a Free Boundary Problem Related to the Fractional Laplacian |
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| Authors: | Ray Yang |
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| Affiliation: | 1. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA
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| 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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