EAN: 9783319128283

SPRINGERBRIEFS IN MATHEMATICS AN INTRODUCTION...

The purpose of this book is to give a quick and elementary  yet rigorous  presentation of the
rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st
and 2nd order Partial Differential Equations (PDE). For such equations  particularly for 2nd
order ones  solutions generally are non-smooth and standard approaches in order to define a
weak solution do not apply: classical  strong almost everywhere  weak  measure-valued and
distributional solutions either do not exist or may not even be defined. The main reason for
the latter failure is that  the standard idea of using integration-by-parts in order to pass
derivatives to smooth test functions by duality  is not available for non-divergence structure
PDE.

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