{"product_id":"degenerate-elliptic-equations-9780792323051","title":"Degenerate Elliptic Equations","description":"\u003cp\u003e • Author(s): Serge Levendorskii\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Differential Equations - Partial\u003c\/p\u003e\u003cp\u003e0.1 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 \u0026gt; 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).\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":46893503414423,"sku":"9780792323051","price":7345.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780792323051.webp?v=1770316765","url":"https:\/\/atlanticbooks.com\/products\/degenerate-elliptic-equations-9780792323051","provider":"Atlantic Books","version":"1.0","type":"link"}