Regularity of the singular set in the fully nonlinear obstacle problem

2019/05/07 by Ovidiu Savin, Hui Yu, Savin, Ovidiu +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1905.02308

openalex publication_date 2019/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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,α-manifold, and the lower strata are covered by C^1,logε-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.

Cited by

• Tangential touch between free and fixed boundaries for the fully nonlinear Alt-Phillips problem
• Remarks on the fine structure of the free boundary (the no-sign obstacle problem)

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