{"product_id":"comparison-principles-for-general-potential-theories-and-pdes-paperback","title":"Comparison Principles for General Potential Theories and Pdes - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eMarco Cirant\u003c\/b\u003e (Author), \u003cb\u003eF. Reese Harvey\u003c\/b\u003e (Author), \u003cb\u003eH. Blaine Lawson\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eAn examination of the symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eIn recent years, there has evolved a symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories. This book examines important aspects of this story. One main purpose is to prove comparison principles for nonlinear potential theories in Euclidian spaces straightforwardly from duality and monotonicity under the weakest possible notion of ellipticity. The book also shows how to deduce comparison principles for nonlinear differential operators, by marrying these two points of view, under the correspondence principle. \u003cp\u003e\u003c\/p\u003eThe authors explain that comparison principles are fundamental in both contexts, since they imply uniqueness for the Dirichlet problem. When combined with appropriate boundary geometries, yielding suitable barrier functions, they also give existence by Perron's method. There are many opportunities for cross-fertilization and synergy. In potential theory, one is given a constraint set of 2-jets that determines its subharmonic functions. The constraint set also determines a family of compatible differential operators. Because there are many such operators, potential theory strengthens and simplifies the operator theory. Conversely, the set of operators associated with the constraint can influence the potential theory.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eMarco Cirant\u003c\/b\u003e is associate professor of mathematical analysis at the Università di Padova. \u003cb\u003eF. Reese Harvey\u003c\/b\u003e is professor emeritus of mathematics at Rice University and the author of \u003ci\u003eSpinors and Calibrations.\u003c\/i\u003e \u003cb\u003eH. Blaine Lawson\u003c\/b\u003e is distinguished professor of mathematics at Stony Brook University, a member of the National Academy of Sciences, and the author of six books, including \u003ci\u003eSpin Geometry\u003c\/i\u003e, with Marie-Louise Michelsohn (Princeton). \u003cb\u003eKevin R. Payne\u003c\/b\u003e is associate professor of mathematical analysis at the Università di Milano and a Fellow of the American Mathematical Society.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 224\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.4 x 9.5 x 6.5 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 03, 2023\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337012134137,"sku":"9780691243627","price":128.25,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/9jA7hQKJ1U9780691243627.webp?v=1769674562","url":"https:\/\/bookscloud.io\/products\/comparison-principles-for-general-potential-theories-and-pdes-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}