Positive solutions for singular elliptic systems with convection term
This paper is concerned with the existence and regularity of solutions of a class of quasilinear elliptic systems with Dirichlet boundary condition. A feature of this paper is the presence of convection (gradient) terms. The main result establishes a sufficient condition for the existence of positive Hölder solutions. The proof combines comparison principles and \textit{a priori} estimates. A key role is to identify the appropriate set where the Schauder fixed point theorem can be applied. The main concern in determining this set is to take into account the behavior of the gradient up to the boundary of the domain. The arguments are very clear and seem to be applicable to other classes of nonlinear elliptic systems.
scientific article; zbMATH DE number 6821169
scientific article