Degenerate Elliptic Equations

Serge Levendorskii (Autor)

Buch | Softcover

436 Seiten

2010 | 1st ed. Softcover of orig. ed. 1993
Springer (Verlag)
978-90-481-4282-8 (ISBN)

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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).

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.

Erscheint lt. Verlag	15.12.2010
Reihe/Serie	Mathematics and Its Applications ; 258
Zusatzinfo	XII, 436 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	210 x 297 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Technik ► Maschinenbau
ISBN-10	90-481-4282-2 / 9048142822
ISBN-13	978-90-481-4282-8 / 9789048142828
Zustand	Neuware