The transmission problem for elliptic second order equations in a conical domain

Abstract

The present article is a survey of our last results. We establish best possible estimates of the weak solutions to the transmission problem near conical boundary point. We study this problem for the Laplace operator with N different media, for linear and quasi-linear (with semi-linear principal part) elliptic second order equations in divergence form. Boundary conditions in these roblems are different: the Dirichlet, the Neumann, the Robin, as well as mixed boundary conditions.