Vol. 9, No. 2, 2016

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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, C1,1-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
Received: 12 June 2015
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