Serguei Samborski

The equation H( x, y, grad y) = f .

Extensions of PD operators from the set of smooth functions in some appropriate functional spaces lead to solutions of corresponding equations which may be discontinuous but physically justified( f.e. shock waves ). General existence results that are new even in the case of Ordinary DE are obtained. We study also "superstability" of these solutions i.e. stability under "singular perturbations" that raise the order of PDE. In some results the only condition for H is its continuity.

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