Free boundary regularity near the fixed boundary for the fully nonlinear obstacle problem

Abstract

The interior free boundary theory for linear elliptic operators in higher dimensions was developed by Caffarelli [Caf77] in the low regularity context. In these notes, the up-to-the boundary free boundary regularity is discussed for nonlinear elliptic operators based on a different approach.

Boundary Regularity and Nontransversal Intersection for the Fully Nonlinear Obstacle Problem

“…After completion of this work, a variant of the problem has been considered in [15] (see also [16]).…”

Tangential contact between free and fixed boundaries for variational solutions to variable coefficient Bernoulli type Free boundary problems

“…Very recently, works of Indrei [12], [13] study interactions of free boundaries and fixed boundaries for fully non-linear obstacle problems. We refer to [10] where authors shed more light into angle of contact between fixed boundary and free boundary for one phase Bernoulli problem.…”