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.
KeywordsMaximum Principle Dirichlet Problem Strong Solution Newtonian Potential Weak Maximum Principle
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