Boundary regularity and non-transversal intersection for the fully nonlinear obstacle problem

Abstract

In this paper non-transversal intersection of the free and fixed boundary is shown to hold in any dimension for obstacle problems generated by fully nonlinear uniformly elliptic operators. Moreover, $C^1$ regularity results of the free boundary are obtained and a classification of blow-up solutions is given.

A version of this paper is accepted for publication in CPAM

References in corpus (3)

• Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems
• Non-transversal intersection of free and fixed boundary for fully nonlinear elliptic operators in two dimensions
• Free boundary regularity near the fixed boundary for the fully nonlinear obstacle problem

Cited by in corpus (3)

• A weighted relative isoperimetric inequality in convex cones
• Sharp Hessian estimates for fully nonlinear elliptic equations under relaxed convexity assumptions, oblique boundary conditions and applications
• On the fully nonlinear Alt-Phillips equation