IUMJ

Title: New maximum principles for linear elliptic equations

Authors: Hung-ju Kuo and Neil Sidney Trudinger

Issue: Volume 56 (2007), Issue 5, 2439-2452

Abstract:

We prove extensions of the estimates of Aleksandrov and Bakel'man for linear elliptic operators in Euclidean space $\mathbb{R}^n$ to inhomogeneous terms in $L^q$ spaces for $q < n$. Our estimates depend on restrictions on the ellipticity of the operators determined by certain subcones of the positive cone. We also consider some applications to local pointwise and $L^2$ estimates.