Degenerate Elliptic Equations
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1993
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| Schriftenreihe: | Mathematics and Its Applications
258 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Beschreibung: | 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 distribution 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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| Beschreibung: | 1 Online-Ressource (XII, 436 p) |
| ISBN: | 9789401712156 9789048142828 |
| DOI: | 10.1007/978-94-017-1215-6 |