IJPAM: Volume 22, No. 2 (2005)

ON STRONG COMPARISON PRINCIPLE FOR
SEMICONTINUOUS VISCOSITY SOLUTIONS OF
SOME NONLINEAR ELLIPTIC EQUATIONS

Yoshikazu Giga$^1$, Masaki Ohnuma$^2$
$^1$Graduate School of Mathematical Sciences
University of Tokyo
Komaba 3-8-1, Meguro, Tokyo, 153-8914, JAPAN
e-mail: labgiga@ms.u-tokyo.ac.jp
$^2$Department of Mathematical and Natural Sciences
The University of Tokushima
Tokushima, 770-8502, JAPAN
e-mail: ohnuma@ias.tokushima-u.ac.jp


Abstract.The strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations are considered. For linear elliptic equations it is well known that the strong comparison principle is equivalent to the strong maximum principle. However, for nonlinear equations the strong maximum principle may not imply the strong comparison principle. We establish a strong comparison principle for some nonlinaer elliptic equations including the minimal surface equation.

Received: May 30, 2005

AMS Subject Classification: 35B05, 35B50, 35J60

Key Words and Phrases: strong comparison principle, viscosity solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 2