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...
Main Authors: | , , , |
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Format: | eBook |
Language: | English |
Published: |
Princeton
Princeton University Press
2023, 2023©2023
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Series: | Annals of mathematics studies
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Subjects: | |
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