Abstract
We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight |y|^a for a in (-1,1). Such problem arises as the local extension of the obstacle problem for the fractional heat operator (partial _t - Delta _x)^s for s in (0,1). Our main result establishes the complete structure and regularity of the singular set of the free boundary. To achieve it, we prove Almgren-Poon, Weiss, and Monneau type monotonicity formulas which generalize those for the case of the heat equation (a=0).
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