3 papers
math.AP2023
Solutions to the nonlinear obstacle problem with compact contact sets
Simon Eberle, Hui Yu
For the obstacle problem with a nonlinear operator, we characterize the space of global solutions with compact contact sets. This is achieved by constructing a bijection onto a cla…
math.AP2023
Compact contact sets of sub-quadratic solutions to the thin obstacle problem
Simon Eberle, Hui Yu
We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution…
math.AP2021
Free boundary regularity in the multiple membrane problem in the plane
Ovidiu Savin, Hui Yu
We study the regularity of free boundaries in the multiple elastic membrane problem in the plane. We prove the uniqueness of blow-ups, and that the free boundaries are …