The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations [electronic resource] /

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.

Bibliographic Details

Main Authors:	Gindikin, S. author., Volevich, L. R. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands : Imprint: Springer, 1992
Subjects:	Mathematics., Mathematical analysis., Analysis (Mathematics)., Partial differential equations., Partial Differential Equations., Analysis.,
Online Access:	http://dx.doi.org/10.1007/978-94-011-1802-6
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