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A Primer on Semiconvex Functions in General Potential Theories

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, i...

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Bibliografske podrobnosti
Main Authors: Payne, Kevin R. (Author), Redaelli, Davide Francesco (Author)
Korporativna značnica: SpringerLink (Online service)
Format: Elektronski eKnjiga
Jezik:angleščina
Izdano: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Izdaja:1st ed. 2025.
Serija:Lecture Notes in Mathematics, 2371
Teme:
Functions of real variables.
Potential theory (Mathematics).
Differential equations.
Real Functions.
Potential Theory.
Differential Equations.
Online dostop:https://doi.org/10.1007/978-3-031-94340-9
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Kazalo:
  • 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.

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