A brief survey on the obstacle problem

2019/10/19 by Hui Yu, Yu, Hui
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1910.08730

openalex publication_date 2019/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss some regularity issues in the study of the obstacle problem. In particular, we present a recent result by O. Savin and the author on the regularity of the singular set for the obstacle problem with a fully nonlinear elliptic operator. This survey is based on a lecture by the author at the 8th International Congress of Chinese Mathematicians.

Citations

• Variational problems with two phases and their free boundaries

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• Regularity of the singular set in the fully nonlinear obstacle problem
• On the fine regularity of the singular set in the nonlinear obstacle problem
• The double obstacle problem on non divergence form
• Regularity theory for nonlocal obstacle problems with critical and subcritical scaling
• The structure of the regular part of the free boundary close to singularities in the obstacle problem