{"product_id":"comparison-principles-for-general-potential-theories-and-pdes-ams-218-9780691243627","title":"Comparison Principles for General Potential Theories and Pdes: (Ams-218)","description":"\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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-15920897\"\u003eMarco Cirant\u003c\/a\u003e, \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-146294\"\u003eF. Reese Harvey\u003c\/a\u003e, \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=AUTH-16040484\"\u003eH. Blaine Lawson\u003c\/a\u003e\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/03\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 224\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.80lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.50h x 6.50w x 1.40d\u003cbr\u003e\u003cb\u003eISBN13:\u003c\/b\u003e 9780691243627\u003cbr\u003e\u003cb\u003eISBN10:\u003c\/b\u003e 069124362X\u003cbr\u003e\u003cb\u003eBISAC Categories:\u003c\/b\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT007000\"\u003eDifferential Equations | General\u003c\/a\u003e\u003cbr\u003e- \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=CAT-MAT\"\u003eMathematics\u003c\/a\u003e | \u003ca href=\"https:\/\/sureshotbooks-com.myshopify.com\/search?type=product%2Carticle%2Cpage\u0026amp;q=BISAC-MAT005000\"\u003eCalculus\u003c\/a\u003e\u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eMarco Cirant\u003c\/b\u003e is associate professor of mathematical analysis at the Università di Padova. \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\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\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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":44704293945581,"sku":"9780691243627","price":118.75,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0550\/8097\/6621\/products\/img_a5475492-2d26-4e11-9ce0-fb969dd8847c.jpg?v=1703912162","url":"https:\/\/sureshotbooks.com\/products\/comparison-principles-for-general-potential-theories-and-pdes-ams-218-9780691243627","provider":"SureShot Books Publishing LLC","version":"1.0","type":"link"}