## 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

Emanuel Indrei and Andreas Minne

#### 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.

#### 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

**Keywords**

obstacle problem tangential touch fully nonlinear equations nontransverse intersection free boundary problem

#### 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