Strong Maximum Principle for Viscosity Solutions of Fully Nonlinear Cooperative Elliptic Systems

In this paper, we consider the validity of strong maximum principle for weakly coupled, degenerate and cooperative elliptic systems in a bounded domain. particular, are interested viscosity solutions with fully nonlinear degenerated principal symbol. Applying method solutions, introduced by Crandall, Ishii Lions 1992, prove interior boundary semi-continuous sub- super-solutions such systems. For first time literature, is considered to As consequence principle, derive comparison case when on them classical one. The main novelty work reduction smoothness solution. literature proved C2 or generalized C1 while it ones.