東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

A primer on semiconvex functions in ...

Payne, Kevin R.

Linked to FindBook

Google Book

Amazon

博客來

A primer on semiconvex functions in general potential theories

Record Type:	Electronic resources : Monograph/item
Title/Author:	A primer on semiconvex functions in general potential theories/ by Kevin R. Payne, Davide Francesco Redaelli.
Author:	Payne, Kevin R.
other author:	Redaelli, Davide Francesco.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xx, 141 p. :ill., digital ;24 cm.
[NT 15003449]:	Part I. Semiconvex apparatus -- Chapter 1. Differentiability of convex functions -- Chapter 2. Semiconvex functions and upper contact jets -- Chapter 3. The lemmas of Jensen and Slodkowski -- Chapter 4. Semiconvex approximation of semicontinuous functions -- Part II. General potential-theoretic analysis -- Chapter 5. General potential theories -- Chapter 6. Duality and monotonicity in general potential theories -- Chapter 7. Basic tools in nonlinear potential theory -- Chapter 8. Semiconvex functions and subharmonics -- Chapter 9. Comparison principles -- Chapter 10. From Euclidean spaces to manifolds: a brief note.
Contained By:	Springer Nature eBook
Subject:	Convex functions. -
Online resource:	https://doi.org/10.1007/978-3-031-94340-9
ISBN:	9783031943409

A primer on semiconvex functions in general potential theories
Payne, Kevin R.

A primer on semiconvex functions in general potential theories[electronic resource] /by Kevin R. Payne, Davide Francesco Redaelli. - Cham :Springer Nature Switzerland :2025. - xx, 141 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23711617-9692 ;. - Lecture notes in mathematics ;v. 2371..

Part I. Semiconvex apparatus -- Chapter 1. Differentiability of convex functions -- Chapter 2. Semiconvex functions and upper contact jets -- Chapter 3. The lemmas of Jensen and Slodkowski -- Chapter 4. Semiconvex approximation of semicontinuous functions -- Part II. General potential-theoretic analysis -- Chapter 5. General potential theories -- Chapter 6. Duality and monotonicity in general potential theories -- Chapter 7. Basic tools in nonlinear potential theory -- Chapter 8. Semiconvex functions and subharmonics -- Chapter 9. Comparison principles -- Chapter 10. From Euclidean spaces to manifolds: a brief note.

This 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. The 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. The 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.

ISBN: 9783031943409

Standard No.: 10.1007/978-3-031-94340-9doiSubjects--Topical Terms:

544201
Convex functions.

LC Class. No.: QA331.5

Dewey Class. No.: 515.8

A primer on semiconvex functions in general potential theories
LDR:03182nmm a2200337 a 4500 001 2414344
003 DE-He213
005 20250807130452.0
006 m d
007 cr nn 008maaau
008 260205s2025 sz s 0 eng d
020 $a 9783031943409 $q (electronic bk.)
020 $a 9783031943393 $q (paper)
024 7 $a 10.1007/978-3-031-94340-9 $2 doi
035 $a 978-3-031-94340-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331.5
072 7 $a PBKB $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKB $2 thema
082 0 4 $a 515.8 $2 23
090 $a QA331.5 $b .P346 2025
100 1 $a Payne, Kevin R. $3 3790985
245 1 2 $a A primer on semiconvex functions in general potential theories $h [electronic resource] / $c by Kevin R. Payne, Davide Francesco Redaelli.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xx, 141 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2371
505 0 $a Part I. Semiconvex apparatus -- Chapter 1. Differentiability of convex functions -- Chapter 2. Semiconvex functions and upper contact jets -- Chapter 3. The lemmas of Jensen and Slodkowski -- Chapter 4. Semiconvex approximation of semicontinuous functions -- Part II. General potential-theoretic analysis -- Chapter 5. General potential theories -- Chapter 6. Duality and monotonicity in general potential theories -- Chapter 7. Basic tools in nonlinear potential theory -- Chapter 8. Semiconvex functions and subharmonics -- Chapter 9. Comparison principles -- Chapter 10. From Euclidean spaces to manifolds: a brief note.
520 $a This 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. The 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. The 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.
650 0 $a Convex functions. $3 544201
650 0 $a Potential theory (Mathematics) $3 558874
650 1 4 $a Real Functions. $3 891265
650 2 4 $a Potential Theory. $3 893956
650 2 4 $a Differential Equations. $3 907890
700 1 $a Redaelli, Davide Francesco. $3 3790986
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2371. $3 3790987
856 4 0 $u https://doi.org/10.1007/978-3-031-94340-9
950 $a Mathematics and Statistics (SpringerNature-11649)