This volume develops the method of Newton's polyhedron for  solving some problems in the theory of partial differential equations.      The content is divided into two parts. Chapters 1-4 consider Newton's  polygon and Chapters 5-7 consider Newton's polyhedron. The case of the  polygon makes it possible not only to consider general constructions  in the two-dimensional case, but also leads to some natural  multidimensional applications. Attention is mainly focused on a  special class of hypoelliptic operators defined using Newton's  polyhedron, energy estimates in Cauchy's problem relating to Newton's  polyhedron, and generalized operators of principal type. Priority is  given to the presentation of an algebraic technique which can be  applied to many other problems as well.     For researchers and graduate students whose work involves the theory  of differential and pseudodifferential equations.

The Method of Newton's Polyhedron in the Theory of Partial Differential Equations (Mathematics and its Applications) PDF

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