{"product_id":"a-primer-on-semiconvex-functions-in-general-potential-theories-von-kevin-r-payne-und-davide-francesco-redaelli","title":"A Primer on Semiconvex Functions in General Potential Theories","description":"\n                                \n                \u003cp\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\/p\u003e\n                                \n                \n                \u003cp\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                                \n                \n                \u003cp\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\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031943393\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783031943393","offer_id":55504974086469,"sku":"9783031943393","price":74.89,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/4c84843b-c373-4a81-8ad5-b503518ac67a.jpg?v=1778817923","url":"https:\/\/shop.autorenwelt.de\/products\/a-primer-on-semiconvex-functions-in-general-potential-theories-von-kevin-r-payne-und-davide-francesco-redaelli","provider":"Autorenwelt Shop","version":"1.0","type":"link"}