Buch, Englisch, 436 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 674 g
Buch, Englisch, 436 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 674 g
Reihe: Mathematics and Its Applications
ISBN: 978-90-481-4282-8
Verlag: Springer Netherlands
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).
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
Weitere Infos & Material
0 Introduction.- 1 General Calculus of Pseudodifferential Operators.- 2 Model Classes of Degenerate Elliptic Differential Operators.- 3 General Classes of Degenerate Elliptic Differential Operators.- 4 Degenerate Elliptic Operators in Non — Power — Like Degeneration Case.- 5 Lp — Theory for Degenerate Elliptic Operators.- 6 Coersiveness of Degenerate Quadratic Forms.- 7 Some Classes of Hypoelliptic Pseudodifferential Operators on Closed Manifold.- 8 Algebra of Boundary Value Problems for Class of Pseudodifferential Operators which Change Order on the Boundary.- 9 General Schemes of Investigation of Spectral Asymptotics for Degenerate Elliptic Equations.- 10 Spectral Asymptotics of Degenerate Elliptic Operators.- 11 Spectral Asymptotics of Hypoelliptic Operators with Multiple Characteristics.- A Brief Review of the Bibligraphy.- Index of Notation.
