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arXiv · 1905.02308

Regularity of the singular set in the fully nonlinear obstacle problem

Ovidiu Savin·Hui Yu
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Abstract

For the obstacle problem involving a convex fully nonlinear elliptic operator, we show that the singular set in the free boundary stratifies. The top stratum is locally covered by a $C^{1,\alpha}$-manifold, and the lower strata are covered by $C^{1,\log^\varepsilon}$-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.

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Ovidiu Savin, Hui Yu. 2019-05-07. Regularity of the singular set in the fully nonlinear obstacle problem. https://arxiv.org/abs/1905.02308

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