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Contact points with integer frequencies in the thin obstacle problem
Ovidiu Savin, Hui Yu
For the thin obstacle problem, we develop a unified approach that leads to rates of convergence to blow-up profiles at contact points with integer frequencies. For these points, we…
On the fine regularity of the singular set in the nonlinear obstacle problem
Ovidiu Savin, Hui Yu
We revisit and sharpen the results from our previous work, where we investigated the regularity of the singular set of the free boundary in the nonlinear obstacle problem. As in th…
On the fully nonlinear Alt-Phillips equation
Yijing Wu, Hui Yu
For a parameter , we study the fully nonlinear version of the Alt-Phillips equation, , for We establish the optimal regularity of the solution…
A brief survey on the obstacle problem
Hui Yu
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 f…
Regularity of the singular set in the fully nonlinear obstacle problem
Ovidiu Savin, Hui Yu
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…
Global estimates for Monge-Ampère equation with natural boundary condition
Ovidiu Savin, Hui Yu
For the Monge-Ampère equation with a right-hand side bounded away from 0 and infinity, we show that the solution, subject to the natural boundary condition arising in optimal trans…