{"product_id":"9781461266563","title":"Progress in Nonlinear Differential Equations and Their Applications","description":"\u003ch1\u003eProgress in Nonlinear Differential Equations and Their Applications\u003c\/h1\u003e \u003ch2\u003eGutierrez, Cristian E.\u003c\/h2\u003e \u003cp\u003eIn recent years, the study of the Monge-Ampere equation has received consider­ able attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to reflect these advances in an essentially self-contained systematic exposi­ tion of the theory of weak: solutions, including recent regularity results by L. A. Caffarelli. The theory has a geometric flavor and uses some techniques from har­ monic analysis such us covering lemmas and set decompositions. An overview of the contents of the book is as follows. We shall be concerned with the Monge-Ampere equation, which for a smooth function u, is given by (0.0.1) There is a notion of generalized or weak solution to (0.0.1): for u convex in a domain n, one can define a measure Mu in n such that if u is smooth, then Mu 2 has density det D u. Therefore u is a generalized solution of (0.0.1) if M u = f.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-10-23\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781461266563\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4612-0195-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 132\u003c\/p\u003e ","brand":"Birkhäuser Boston","offers":[{"title":"Default Title","offer_id":44343310712972,"sku":"9781461266563","price":80.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461266563.jpg?v=1772024243","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781461266563","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}