The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations (Mathematics and its Applications, 86)

Gindikin, S.G.; Volevich, L.

ISBN 10: 0792320379 / ISBN 13: 9780792320371

Published by Springer, 1992

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Seller Inventory # I-9780792320371

Bibliographic Details

• Title: The Method of Newton?s Polyhedron in the Theory of Partial Differential Equations (Mathematics and its Applications, 86)
• Publisher: Springer
• Publication Date: 1992
• Language: English
• ISBN 10: 0792320379
• ISBN 13: 9780792320371
• Binding: Hardcover
• Condition: New

About this title

Synopsis

One service mathematics has rendered the 'Et moi, .. ., si j'avait su comment cn rcvenir, human race. It has put common sense back. je n'y serais point aile.' where it bdongs, on the topmost shelf neAt Jules Verne to the dusty canister labelled 'discarded non· sense'. The series is divergent; therefore we may be Eric T. Bdl able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. :; 'One service category theory has rendered mathematics .. .'. All a,rguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Synopsis

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 makes it possible not only to consider general constructions in the two-dimensional case, but also leads to some natural multidmensional 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, 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.