Abstract
Beginning with this chapter we develop the method of Newton’s polyhedron in the theory of differential equations. The passage from Newton’s polygon to Newton’s polyhedron is quite natural. For polynomials we consider the convex hull of the set of monomial multiexponents completed in a certain way. In the present chapter we are interested in conditions under which the polynomials admit of an adequate estimate by means of the sum of the moduli of the constituent monomials. Of course, this relates to adequate estimates for differential operators whose symbols possess the indicated property.
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© 1992 Springer Science+Business Media Dordrecht
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Gindikin, S., Volevich, L.R. (1992). Two-Sided Estimates in Several Variables Relating to Newton’s Polyhedra. In: The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations. Mathematics and Its Applications(Soviet Series), vol 86. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1802-6_5
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DOI: https://doi.org/10.1007/978-94-011-1802-6_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4794-4
Online ISBN: 978-94-011-1802-6
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