IJPAM: Volume 57, No. 3 (2009)

A STRONG MAXIMUM PRINCIPLE FOR
LINEAR ELLIPTIC OPERATORS

Paola Cavaliere$^1$, Maria Transirico$^2$
$^1$Department of Engineering of Information and Applied Mathematics
University of Salerno
Via Ponte Don Melillo, Fisciano (Salerno), I-84084, ITALY
e-mail: pcavaliere@unisa.it
$^2$Department of Mathematics and Informatics
University of Salerno
Via Ponte Don Melillo, Fisciano (Salerno), I-84084, ITALY
e-mail: mtransirico@unisa.it


Abstract.This paper is concerned with a maximum principle for subsolutions, in the class $W_{\mbox{\rm loc}}^{2,p}$, of second order linear elliptic equations in non-divergence form in arbitrary open (bounded or not) subsets of ${\mathbb R}^n$, $n\geq2$, when $p>{n\over2}$.

The main coefficients are required to be just locally in $L^{\infty} \cap VMO$. A uniqueness result for the related homogenous Dirichlet problem is also obtained.

Received: October 4, 2006

AMS Subject Classification: 35J25, 35R05

Key Words and Phrases: elliptic operators, VMO-coefficients

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 3