Dept. Math, Hokkaido Univ. EPrints Server

On strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations

Preprint Series # 719
Giga, Yoshikazu and Ohnuma, Masaki On strong comparison principle for semicontinuous viscosity solutions of some nonlinear elliptic equations. (2005);

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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.

Item Type:Preprint
Uncontrolled Keywords:strong comparison principle, viscosity solutions
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:952