The existence of strong solution for a nonlinear elliptic equation

Abstract

Abstract In this paper, the existence of strong solution for a fully nonlinear elliptic equation is proved by using the acute angle principle for the compulsorily weakly continuous operator. Firstly, the space of function and the abstract operator are chosen according to the elliptic equation. Furthermore, it is proved that the operator satisfies the acute angle condition and is compulsorily weakly continuous. Thus the existence of strong solution for the nonlinear elliptic equation is obtained.