## Analysis & PDE

• Anal. PDE
• Volume 9, Number 2 (2016), 487-502.

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

#### 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.

#### Article information

Source
Anal. PDE, Volume 9, Number 2 (2016), 487-502.

Dates
Received: 12 June 2015
Revised: 6 January 2016
Accepted: 9 February 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843244

Digital Object Identifier
doi:10.2140/apde.2016.9.487

Mathematical Reviews number (MathSciNet)
MR3513142

Zentralblatt MATH identifier
1341.35054

Subjects
Primary: 35JXX 35QXX
Secondary: 49SXX

#### Citation

Indrei, Emanuel; Minne, Andreas. Nontransversal intersection of free and fixed boundaries for fully nonlinear elliptic operators in two dimensions. Anal. PDE 9 (2016), no. 2, 487--502. doi:10.2140/apde.2016.9.487. https://projecteuclid.org/euclid.apde/1510843244

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