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Comparison principles for general potential theories and PDEs

"In this monograph, Cirant et al. prove comparison principles for nonlinear potential theories in Euclidian spaces in a straightforward manner from duality and monotonicity. They also show how to deduce comparison principles for nonlinear differential operators--a program seemingly different fr...

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Bibliographic Details
Main Authors: Cirant, Marco, Harvey, F. Reese (Author), Lawson, H. Blaine (Author), Payne, Kevin R. (Author)
Format: eBook
Language:English
Published: Princeton Princeton University Press 2023, 2023©2023
Series:Annals of mathematics studies
Subjects:
Nonlinear Operators
Differential Equations, Partial
Mathematics / Differential Equations / General
Potential Theory (mathematics)
Online Access:
Collection: JSTOR Books - Collection details see MPG.ReNa
Table of Contents:
  • Includes bibliographical references and index
  • A comprehensive introduction
  • Constant-coefficient constraint sets and their subharmonics
  • Dirichlet duality and f-subharmonic functions
  • Monotonicity cones for constant-coefficient subequations
  • A fundamental family of monotonicity cone subequations
  • The zero maximum principle for dual monotonicity cones
  • The comparison principle for m-monotone subequations
  • Comparison on arbitrary domains by additional monotonicity
  • Failure of comparison with insufficient maximal monotonicity
  • Special cases : reduced constraint sets
  • Subequation constraint sets and nonlinear operators
  • Comparison principles for nonlinear operators

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