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تسجيل مستخدم جديدStructure and regularity of the singular set in the obstacle problem for the fractional Laplacian
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We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, $minbigl{(-Delta)^su,,u-varphibigr}=0$ in $mathbb R^n$, for general obstacles $varphi$. Our main result establishes the complete structure and regularity of the singular set. To prove it, we construct new monotonicity formulas of Monneau-type that extend those in cite{GP} to all $sin(0,1)$.
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