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Publication 119

Non-transversal intersection of free and fixed boundary for fully nonlinear elliptic operators in two dimensions


CMUE. Indrei
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh PA 15213-3890 USA

Andreas Minne
Department of Mathematics
KTH, Royal Institute of Technology
100 44 Stockholm, Sweden

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 boundary in two dimensions for fully nonlinear elliptic operators. Along the way, several n-dimensional results of independent interest are obtained such as BMO- estimates, C1,1 regularity up to the fixed boundary, and a description of the behavior of blow-up solutions.
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