2 papers
math.AP2025
Linearized equation and generic regularity in the Alt-Caffarelli problem
Xavier Fernández-Real, Hui Yu
For the Alt-Caffarelli problem, we study free boundary regularity of energy minimizers. In six dimensions, we show that free boundaries are analytic for generic boundary data. In g…
math.AP2025
Global solutions to the thin obstacle problem with superquadratic growth
Xavier Fernández-Real, Hui Yu
We study rigidity/flexibility properties of global solutions to the thin obstacle problem. For solutions with bounded positive sets, we give a classification in terms of their expa…