Development of local, global, and trace estimates for the solutions of elliptic equations (Q1599951)

This paper deals with the local, global, and trace estimates for the solutions of elliptic equations. The author develops these estimates for the solutions of elliptic second-order equations with source terms, with Dirichlet-Neumann boundary conditions, and Dirichlet boundary conditions. They are obtained under quasi-optimal regularity conditions on the source terms. Note that the trace estimates developed by the author are useful in the study of fixed point, the treatment of contraction properties of some operators, and also for the analysis of algorithms in numerical analysis.