{"product_id":"degenerate-elliptic-equations-von-serge-levendorskii","title":"Degenerate Elliptic Equations","description":"\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\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048142828\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792323051\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9789048142828","offer_id":39415669653597,"sku":"9789048142828","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9780792323051","offer_id":50827335878,"sku":"9780792323051","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/935ef08f-fca9-448c-a34e-c41f984d52bf.jpg?v=1775103491","url":"https:\/\/shop.autorenwelt.de\/en\/products\/degenerate-elliptic-equations-von-serge-levendorskii","provider":"Autorenwelt Shop","version":"1.0","type":"link"}