Comparison principles for general potential theories and PDEs:
Gespeichert in:
| Beteiligte Personen: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton ; Oxford
Princeton University Press
[2023]
|
| Schriftenreihe: | Annals of Mathematics Studies
Number 218 |
| 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: | xiv, 203 Seiten |
| ISBN: | 9780691243610 9780691243627 |
Internformat
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| 100 | 1 | |a Cirant, Marco |d 1986- |0 (DE-588)1306102197 |4 aut | |
| 245 | 1 | 0 | |a Comparison principles for general potential theories and PDEs |c Marco Cirant, F. Reese Harvey, H. Blaine Lawson, Kevin R. Payne |
| 264 | 1 | |a Princeton ; Oxford |b Princeton University Press |c [2023] | |
| 300 | |a xiv, 203 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Annals of Mathematics Studies |v Number 218 | |
| 520 | 3 | |a 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. | |
| 700 | 1 | |a Harvey, Frank Reese |d 1941- |0 (DE-588)172127580 |4 aut | |
| 700 | 1 | |a Lawson, H. Blaine |d 1942- |0 (DE-588)122158814 |4 aut | |
| 700 | 1 | |a Payne, Kevin R. |d 1962- |0 (DE-588)1306107318 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-691-24364-1 |
| 830 | 0 | |a Annals of Mathematics Studies |v Number 218 |w (DE-604)BV000000991 |9 218 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-034772236 | |
Datensatz im Suchindex
| _version_ | 1818991528771584000 |
|---|---|
| any_adam_object | |
| author | Cirant, Marco 1986- Harvey, Frank Reese 1941- Lawson, H. Blaine 1942- Payne, Kevin R. 1962- |
| author_GND | (DE-588)1306102197 (DE-588)172127580 (DE-588)122158814 (DE-588)1306107318 |
| author_facet | Cirant, Marco 1986- Harvey, Frank Reese 1941- Lawson, H. Blaine 1942- Payne, Kevin R. 1962- |
| author_role | aut aut aut aut |
| author_sort | Cirant, Marco 1986- |
| author_variant | m c mc f r h fr frh h b l hb hbl k r p kr krp |
| building | Verbundindex |
| bvnumber | BV049426011 |
| classification_rvk | SI 830 |
| ctrlnum | (OCoLC)1409640410 (DE-599)BVBBV049426011 |
| dewey-full | 515.96 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.96 |
| dewey-search | 515.96 |
| dewey-sort | 3515.96 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV049426011 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T20:11:42Z |
| institution | BVB |
| isbn | 9780691243610 9780691243627 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034772236 |
| oclc_num | 1409640410 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM |
| owner_facet | DE-19 DE-BY-UBM |
| physical | xiv, 203 Seiten |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Cirant, Marco 1986- (DE-588)1306102197 aut Comparison principles for general potential theories and PDEs Marco Cirant, F. Reese Harvey, H. Blaine Lawson, Kevin R. Payne Princeton ; Oxford Princeton University Press [2023] xiv, 203 Seiten txt rdacontent n rdamedia nc rdacarrier Annals of Mathematics Studies Number 218 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. Harvey, Frank Reese 1941- (DE-588)172127580 aut Lawson, H. Blaine 1942- (DE-588)122158814 aut Payne, Kevin R. 1962- (DE-588)1306107318 aut Erscheint auch als Online-Ausgabe 978-0-691-24364-1 Annals of Mathematics Studies Number 218 (DE-604)BV000000991 218 |
| spellingShingle | Cirant, Marco 1986- Harvey, Frank Reese 1941- Lawson, H. Blaine 1942- Payne, Kevin R. 1962- Comparison principles for general potential theories and PDEs Annals of Mathematics Studies |
| title | Comparison principles for general potential theories and PDEs |
| title_auth | Comparison principles for general potential theories and PDEs |
| title_exact_search | Comparison principles for general potential theories and PDEs |
| title_full | Comparison principles for general potential theories and PDEs Marco Cirant, F. Reese Harvey, H. Blaine Lawson, Kevin R. Payne |
| title_fullStr | Comparison principles for general potential theories and PDEs Marco Cirant, F. Reese Harvey, H. Blaine Lawson, Kevin R. Payne |
| title_full_unstemmed | Comparison principles for general potential theories and PDEs Marco Cirant, F. Reese Harvey, H. Blaine Lawson, Kevin R. Payne |
| title_short | Comparison principles for general potential theories and PDEs |
| title_sort | comparison principles for general potential theories and pdes |
| volume_link | (DE-604)BV000000991 |
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