#### Vol. 9, No. 2, 2016

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Nontransversal intersection of free and fixed boundaries for fully nonlinear elliptic operators in two dimensions

### Emanuel Indrei and Andreas Minne

Vol. 9 (2016), No. 2, 487–502
##### Abstract

In the study of classical obstacle problems, it is well known that in many configurations, the free boundary intersects the fixed boundary tangentially. The arguments involved in producing results of this type rely on the linear structure of the operator. In this paper, we employ a different approach and prove tangential touch of free and fixed boundaries in two dimensions for fully nonlinear elliptic operators. Along the way, several $n$-dimensional results of independent interest are obtained, such as BMO-estimates, ${C}^{1,1}$-regularity up to the fixed boundary, and a description of the behavior of blow-up solutions.

##### Keywords
obstacle problem, tangential touch, fully nonlinear equations, nontransverse intersection, free boundary problem
##### Mathematical Subject Classification 2010
Primary: 35JXX, 35QXX
Secondary: 49SXX
##### Milestones
Revised: 6 January 2016
Accepted: 9 February 2016
Published: 24 March 2016
##### Authors
 Emanuel Indrei Center for Nonlinear Analysis Carnegie Mellon University Pittsburgh, PA 15213 United States Andreas Minne Department of Mathematics KTH Royal Institute of Technology 100 44 Stockholm Sweden