## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2011 (2011), Article ID 453727, 18 pages.

### Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity

#### Abstract

We deal with fully nonlinear second-order equations assuming a superlinear growth in *u* with the aim to generalize previous existence and uniqueness results of viscosity solutions in the whole space without conditions at infinity. We also consider the solvability of the Dirichlet problem in bounded and unbounded domains and show a blow-up result.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2011 (2011), Article ID 453727, 18 pages.

**Dates**

Received: 4 May 2011

Accepted: 8 September 2011

First available in Project Euclid: 25 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1485313258

**Digital Object Identifier**

doi:10.1155/2011/453727

**Mathematical Reviews number (MathSciNet)**

MR2854945

**Zentralblatt MATH identifier**

1237.35041

#### Citation

Galise, G.; Vitolo, A. Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity. Int. J. Differ. Equ. 2011 (2011), Article ID 453727, 18 pages. doi:10.1155/2011/453727. https://projecteuclid.org/euclid.ijde/1485313258