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Degenerate Elliptic Equations
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(Buch) |
Dieser Artikel gilt, aufgrund seiner Grösse, beim Versand als 3 Artikel!
Lieferstatus: |
i.d.R. innert 7-14 Tagen versandfertig |
Veröffentlichung: |
Dezember 2010
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Genre: |
Schulbücher |
ISBN: |
9789048142828 |
EAN-Code:
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9789048142828 |
Verlag: |
Springer Netherlands |
Einband: |
Kartoniert |
Sprache: |
English
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Dimensionen: |
H 235 mm / B 155 mm / D 25 mm |
Gewicht: |
674 gr |
Seiten: |
448 |
Zus. Info: |
Paperback |
Bewertung: |
Titel bewerten / Meinung schreiben
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Inhalt: |
0.1 The partial differential equation (1) (Au)(x) = L aa(x)(Dau)(x) = f(x) m lal9 is called elliptic on a set G, provided that the principal symbol a2m(X,¿) = L aa(x)¿a lal=2m of the operator A is invertible on G X (~n \ 0); A is called elliptic on G, too. This definition works for systems of equations, for classical pseudo differential operators ("pdo), and for operators on a manifold n. Let us recall some facts concerning elliptic operators. 1 If n is closed, then for any s E ~ , is Fredholm and the following a priori estimate holds (2) 1 2 Introduction If m > 0 and A : C=(O; C') -+ L (0; C') is formally self - adjoint 2 with respect to a smooth positive density, then the closure Ao of A is a self - adjoint operator with discrete spectrum and for the distribu tion functions of the positive and negative eigenvalues (counted with multiplicity) of Ao one has the following Weyl formula: as t -+ 00, (3) n 2m = t / II N±(1,a2m(x,e))dxde T·O\O (on the right hand side, N±(t,a2m(x,e))are the distribution functions of the matrix a2m(X,e) : C' -+ CU). |
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