Name: Degenerate Elliptic Equations
Price: 199.36 CAD
Availability: click-8910566-13710633?url=https%3A%2F%2Fwww.chapters.indigo.ca%2Fen-ca%2Fbooks%2Fproduct%2F9789048142828-item.html
Author: Serge Levendorskii
ISBN: 9789401712156

Degenerate Elliptic Equations

by Serge Levendorskii 2020-09-19 11:24:51

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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)''... Read more

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). Less

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