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The method of Newton's polyhedron in the theory of partial differential equations

Author: S G Gindikin; L R Volevich
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers, ©1992.
Series: Mathematics and its applications (Kluwer Academic Publishers)., Soviet series ;, 86.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Develops the method of Newton's polyhedron for solving some problems in the theory of partial differential equations. The first part of the text considers Newton's polygon and the second section  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: S G Gindikin; L R Volevich
ISBN: 0792320379 9780792320371
OCLC Number: 26809661
Description: x, 266 pages : illustrations ; 25 cm.
Contents: 1. Two-sided estimates for polynomials related to Newton's polygon and their application to studying local properties of partial differential operators in two variables.- 1. Newton's polygon of a polynomial in two variables.- 2. Polynomials admitting of two-sided estimates.- 3. N Quasi-elliptic polynomials in two variables.- 4. N Quasi-elliptic differential operators.- Appendix to 4.- 2. Parabolic operators associated with Newton's polygon.- 1. Polynomials correct in Petrovski?'s sense.- 2. Two-sided estimates for polynomials in two variables satisfying Petrovski?'s condition. N-parabolic polynomials.- 3. Cauchy's problem for N-stable correct and N-parabolic differential operators in the case of one spatial variable.- 4. Stable-correct and parabolic polynomials in several variables.- 5. Cauchy's problem for stable-correct differential operators with variable coefficients.- 3. Dominantly correct operators.- 1. Strictly hyperbolic operators.- 2. Dominantly correct polynomials in two variables.- 3. Dominantly correct differential operators with variable coefficients (the case of two variables).- 4. Dominantly correct polynomials and the corresponding differential operators (the case of several spatial variables).- 4. Operators of principal type associated with Newton's polygon.- 1. Introduction. Operators of principal and quasi-principal type.- 2. Polynomials of N-principal type.- 3. The main L2 estimate for operators of N-principal type.- Appendix to 3.- 4. Local solvability of differential operators of N-principal type.- Appendix to 4.- 5. Two-sided estimates in several variables relating to Newton's polyhedra.- 1. Estimates for polynomials in ?n relating to Newton's polyhedra.- 2. Two-sided estimates in some regions in ?n relating to Newton's polyhedron. Special classes of polynomials and differential operators in several variables.- 6. Operators of principal type associated with Newton's polyhedron.- 1. Polynomials of N-principal type.- 2. Estimates for polynomials of N-principal type in regions of special form.- 3. The covering of ?n by special regions associated with Newton's polyhedron.- 4. Differential operators of ?n-principal type with variable coefficients.- Appendix to 4.- 7. The method of energy estimates in Cauchy's problem 1. Introduction. The functional scheme of the proof of the solvability of Cauchy's problem.- 2. Sufficient conditions for the existence of energy estimates.- 3. An analysis of conditions for the existence of energy estimates.- 4. Cauchy's problem for dominantly correct differential operators.- References.
Series Title: Mathematics and its applications (Kluwer Academic Publishers)., Soviet series ;, 86.
Responsibility: by S. Gindikin and L.R. Volevich.
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