TL;DR
This survey reviews recent advances in the regularity theory of the obstacle problem, focusing on singular set regularity for fully nonlinear elliptic operators, highlighting key results and open questions.
Contribution
It presents a recent result on the regularity of the singular set for the obstacle problem with fully nonlinear elliptic operators, advancing understanding in this area.
Findings
Regularity results for the singular set in obstacle problems
Extension of regularity theory to fully nonlinear elliptic operators
Discussion of open problems and future directions
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.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems