Buchumschlag
Comparison Principles for General Potential Theories and PDEs:
Gespeichert in:
Bibliographische Detailangaben
Beteiligte Personen: Cirant, Marco 1986- (VerfasserIn), Harvey, Frank Reese 1941- (VerfasserIn), Lawson, H. Blaine 1942- (VerfasserIn), Payne, Kevin R. 1962- (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Princeton and Oxford Princeton University Press [2023]
Schriftenreihe:Annals of Mathematics Studies Number 218
Links:https://doi.org/10.1515/9780691243641
Abstract:Cover -- Contents -- Preface -- Guide for the Reader -- I. A Comprehensive Introduction -- 1. A Comprehensive Introduction -- 1.1 The Potential Theory Setting -- 1.2 The Differential Operator Setting -- 1.3 The Correspondence Principle -- 1.4 Canonical Operators -- 1.5 Gradient-Free Operators -- 1.6 Operators Involving Gårding-Dirichlet Polynomials -- 1.7 General Potential-Theoretic Comparison Theorems -- 1.8 Limitations of the Method and Comparison with the Literature -- 1.9 Reflections on "Potential Theory versus Operator Theory" -- II. The Potential Theory Approach -- 2. Constant-Coefficient Constraint Sets and Their Subharmonics -- 3. Dirichlet Duality and F-Subharmonic Functions -- 4. Monotonicity Cones for Constant-Coefficient Subequations -- 4.1 The Maximal Monotonicity Cone Subequation -- 4.2 Product Monotonicity Cone Subequations -- 5. A Fundamental Family of Monotonicity Cone Subequations -- 5.1 Construction of the Fundamental Family -- 5.2 Nesting, Limit Cases, and Simplifying the Family of Cones -- 5.3 The Fundamental Nature of the Family of Monotonicity Cones -- 6. The Zero Maximum Principle for Dual Monotonicity Cones -- 7. Comparison Principles for Potential Theories with Sufficient Monotonicity -- 8. Comparison on Arbitrary Domains by Additional Monotonicity -- 9. Failure of Comparison with Insufficient Maximal Monotonicity -- 9.1 Finite R and Failure of Comparison on Large Domains -- 9.2 Failure of Comparison on Arbitrarily Small Domains -- 10. Special Cases: Reduced Constraint Sets -- 10.1 Pure Second Order -- 10.2 Gradient-Free -- 10.3 First Order and Pure First Order -- 10.4 Zero-Order-Free -- 10.5 Summary -- III. Marrying Potential Theory to Operator Theory via the Correspondence Principle -- 11. The Correspondence Principle for Compatible Operator-Subequation Pairs.
Umfang:1 Online-Ressource (xiv, 203 Seiten)
ISBN:9780691243641
DOI:10.1515/9780691243641

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