Overview

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.

Full Product Details

Author:   Semen G. Gindikin ,  L. R. Volevich ,  V. M. Volosov
Publisher:   Kluwer Academic Publishers
Imprint:   Kluwer Academic Publishers
Edition:   1992 ed.
Volume:   86
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.260kg
ISBN:  

9780792320371

ISBN 10:   0792320379
Pages:   266
Publication Date:   30 November 1992
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of 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 insome 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.

Reviews

Author Information

Tab Content 6

Author Website:  

Countries Available

All regions