{"product_id":"9783031943393","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003ePayne, Kevin R.; Redaelli, Davide Francesco\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp class=\"x_x_elementToProof\"\u003e\u003cspan data-olk-copy-source=\"MessageBody\"\u003eThis book examines the symbiotic interplay between fully nonlinear elliptic partial differential equations and general potential theories of second order. Starting with a self-contained presentation of the classical theory of first and second order differentiability properties of convex functions, it collects a wealth of results on how to treat second order differentiability in a pointwise manner for merely semicontinuous functions.  The exposition features an analysis of upper contact jets for semiconvex functions, a proof of the equivalence of two crucial, independently developed lemmas of Jensen (on the viscosity theory of PDEs) and Slodkowski (on pluripotential theory), and a detailed description of the semiconvex approximation of upper semicontinuous functions. \u003c\/span\u003e\u003c\/p\u003e\n\u003cp class=\"x_x_elementToProof\"\u003eThe foundations of general potential theories are covered, with a review of monotonicity and duality, and the basic tools in the viscosity theory of generalized subharmonics, culminating in an account of the monotonicity-duality method for proving comparison principles. The final section shows that the notion of semiconvexity extends naturally to manifolds. A complete treatment of important background results, such as Alexandrov’s theorem and a Lipschitz version of Sard’s lemma, is provided in two appendices.\u003c\/p\u003e\n\u003cp class=\"x_x_elementToProof\"\u003eThe book is aimed at a wide audience, including professional mathematicians working in fully nonlinear PDEs, as well as master’s and doctoral students with an interest in mathematical analysis.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2025-08-07\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031943393\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-94340-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 141\u003c\/p\u003e ","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":44309069070476,"sku":"9783031943393","price":71.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031943393.jpg?v=1779500795","url":"https:\/\/lateknightbooks.com\/products\/9783031943393","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}