Primer on Semiconvex Functions in General Potential Theories

AvKevin R. Payne,Davide Francesco Redaelli

Häftad, Engelska, 2025

Del 2371 i serien Lecture Notes in Mathematics

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Beskrivning

This book examines the symbiotic interplay between fully nonlinear elliptic partial differential equations and general potential theories of second order.

Produktinformation

Utgivningsdatum:2025-08-07
Mått:155 x 235 x 10 mm
Vikt:260 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:141
Förlag:Springer International Publishing AG
ISBN:9783031943393

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Kevin R. Payne is a full professor of mathematical analysis at the Università di Milano and a Fellow of the American Mathematical Society. He received a BA in Mathematics at Rice University and a PhD in Mathematics at Stony Brook University. He is the author of the book Comparison Principles for General Potential Theories and PDEs (Annals of Mathematics Studies 218, Princeton University Press) with Marco Cirant, Reese Harvey and Blaine Lawson.Davide Francesco Redaelli is a post-doc research associate in mathematics at the University of Rome Tor Vergata. He received a MSc in Mathematics at the University of Milan, under the supervision of Prof. Kevin R. Payne, and a PhD in Mathematics at the University of Padua, under the supervision of Prof. Marco Cirant. These Lecture Notes are an improved version of the main chapters of his Master’s Thesis.

Innehållsförteckning

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.