## Differential and Integral Equations

### The Aleksandrov-Bakelman-Pucci maximum principle of fully nonlinear equations for small data and its applications

Kazushige Nakagawa

#### Abstract

The Aleksandrov--Bakelman--Pucci maximum principle is established for $L^p$-viscosity solutions of fully nonlinear second-order elliptic PDEs having linear and superlinear growth terms for the first derivatives with small coefficients.

#### Article information

Source
Differential Integral Equations, Volume 26, Number 11/12 (2013), 1379-1396.

Dates
First available in Project Euclid: 4 September 2013

https://projecteuclid.org/euclid.die/1378327431

Mathematical Reviews number (MathSciNet)
MR3129014

Zentralblatt MATH identifier
1313.35037

Subjects
Primary: 35B50: Maximum principles 35D40: Viscosity solutions

#### Citation

Nakagawa, Kazushige. The Aleksandrov-Bakelman-Pucci maximum principle of fully nonlinear equations for small data and its applications. Differential Integral Equations 26 (2013), no. 11/12, 1379--1396. https://projecteuclid.org/euclid.die/1378327431