| Degenerate Elliptic Equations 1993 Edition Contributor(s): Levendorskii, Serge (Author) |
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ISBN: 079232305X ISBN-13: 9780792323051 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: June 1993 Annotation: This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Gerding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - Partial - Mathematics | Mathematical Analysis - Technology & Engineering | Mechanical |
| Dewey: 515.353 |
| LCCN: 93013188 |
| Series: NATO Asi Series |
| Physical Information: 1" H x 6.14" W x 9.21" (1.78 lbs) 436 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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). |