Strong Solutions

Abstract

Until now in this work we have concentrated on either weak or classical solutions of second-order elliptic equations; a weak solution need only be once weakly differentiable while a classical solution must be at least twice continuously differ-entiable. The formulation of the weak solution concept depended on the operator L under consideration having a “divergence form” while the concept of classical solution made sense for operators with completely arbitrary coefficients. In this chapter our concern is with the intermediate situation of strong solutions.