The Method of Newtons Polyhedron in the Theory of Partial Differential Equations (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
266
Utgivningsdatum
2012-09-27
Upplaga
Softcover reprint of the original 1st ed. 1992
Förlag
Springer
Medarbetare
Volevich, L.
Illustrationer
X, 266 p.
Dimensioner
234 x 156 x 15 mm
Vikt
400 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9789401047944

The Method of Newtons Polyhedron in the Theory of Partial Differential Equations

av S G Gindikin, L Volevich
Häftad,  Engelska, 2012-09-27
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One service mathematics has rendered the 'Et moi, ..., si j'avait su comment cn rcvenir, human race. It has put common sense back. je n'y serais point aile.' where it bdongs, on the topmost shelf neAt Jules Verne to the dusty canister labelled 'discarded non* sense'. The series is divergent; therefore we may be Eric T. Bdl able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science .. :; 'One service category theory has rendered mathematics ...'. All a,rguably true. And all statements obtainable this way form part of the raison d'etre of this series.
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Innehållsförteckning

1. Two-sided estimates for polynomials related to Newtons polygon and their application to studying local properties of partial differential operators in two variables.- 1. Newtons 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 Newtons 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. Cauchys 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. Cauchys 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 Newtons 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 Newtons polyhedra.- 1. Estimates for polynomials in ?n relating to Newtons polyhedra.- 2. Two-sided estimates insome regions in ?n relating to Newtons polyhedron. Special classes of polynomials and differential operators in several variables.- 6. Operators of principal type associated with Newtons 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 Newtons polyhedron.- 4. Differential operators of ?n-principal type with variable coefficients.- Appendix to 4.- 7. The method of energy estimates in Cauchys problem 1. Introduction. The functional scheme of the proof of the solvability of Cauchys problem.- 2. Sufficient conditions for the existence of energy estimates.- 3. An analysis of conditions for the existence of energy estimates.- 4. Cauchys problem for dominantly correct differential operators.- References.

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