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＜電子ブック＞
The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations / by S.G. Gindikin, L. Volevich
(Mathematics and its Applications, Soviet Series ; 86)

版	1st ed. 1992.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1992
本文言語	英語
大きさ	X, 266 p : online resource
著者標目	*Gindikin, S.G author Volevich, L author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical analysis FREE:Differential Equations FREE:Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-94-011-1802-6

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