Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1990
|
| Series: | Lecture notes in mathematics
1445 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 123 S. |
| ISBN: | 3540531033 0387531033 |
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MARC
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| 245 | 1 | 0 | |a Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions |c Friedmar Schulz |
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Record in the Search Index
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TABLE OF CONTENTS
Preface v
Introduction ix
Basic notation *v
Chapter 1. Integral criteria for Holder continuity 1
1.1. Sobolev functions 1
1.2. The Dirichlet growth theorem 2
1.3. Poincare' inequalities 3
1.4. Integral characterizations of the Holder spaces 5
1.5. A Sobolev inequality 10
1.6. The Courant Lebesgue lemma 11
Chapter 2. Regularity for linear elliptic equations and quasilinear systems 15
2.1. Linear homogeneous equations with constant coefficients 15
2.2. Linear equations with constant coefficients 18
2.3. Linear equations with Holder continuous coefficients 21
2.4. Quasilinear elliptic systems of diagonal form 23
Chapter 3. Regularity for Monge Ampere equations 28
3.1. Ellipticity and convexity 28
3.2. A Legendre like transformation 30
3.3. The equation rt s2 = f 33
3.4. The general Monge Ampere equation 34
Chapter 4. Function theory of elliptic equations 39
4.1. Hadamard's integral estimates 39
4.2. The nonhomogeneous Cauchy Riemann system 40
4.3. Regularity for the nonhomogeneous Cauchy Riemann system 43
4.4. The similarity principle 47
4.5. Harnack type inequalities for pseudoanalytic functions 50
Chapter 5. Univalent solutions of binary elliptic systems 53
5.1. Estimates for the gradient from below 53
5.2. Estimates for the Jacobian from below 55
VIII
Chapter 6. Conformal mappings with respect to a Riemannian metric 61
6.1. The Cauchy Riemann Beltrami system 61
6.2. Existence of locally uniformizing parameters 65
6.3. Uniformization and second order elliptic systems 66
6.4. Metrics with Holder continuous and measurable coefficients 70
Chapter 7. Local behavior of solutions of differential inequalities 72
7.1. The Carleman Hartman Wintner theorem 72
7.2. Generalization to differential inequalities with Holder continuous coefficients 75
7.3. The unique continuation principle 81
7.4. Local behavior of solutions of differential inequalities 82
Chapter 8. Univalent solutions of Heinz Lewy type systems 85
8.1. Elliptic systems of Heinz Lewy type 85
8.2. Non vanishing of the Jacobian 89
8.3. Estimates for the Jacobian from below 91
Chapter 9. A priori estimates for Monge Ampere equations 94
9.1. Characteristic parameters for nonlinear elliptic equations 94
9.2. Characteristic parameters for Monge Ampere equations 94
9.3. A priori estimates 97
9.4. Estimates for a general class of Monge 4mpere equations 101
9.5. The Heinz Lewy counterexample 104
Chapter 10. Regularity and a priori estimates for locally convex surfaces 106
10.1. Fundamental formulas in classical surface theory 106
10.2. The prescribed Gaufi curvature equation 108
10.3. The Darboux equation and the regularity of locally convex surfaces 109
10.4. Conjugate isothermal parameters and the Darboux system 110
10.5. A priori estimates for locally convex surfaces 112
References 115
Notation index 121
Subject index 122 |
| any_adam_object | 1 |
| author | Schulz, Friedmar 1952- |
| author_GND | (DE-588)109382145 |
| author_facet | Schulz, Friedmar 1952- |
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| id | DE-604.BV004070296 |
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| indexdate | 2024-07-20T07:36:56Z |
| institution | BVB |
| isbn | 3540531033 0387531033 |
| language | English |
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| physical | XV, 123 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Schulz, Friedmar 1952- Verfasser (DE-588)109382145 aut Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions Friedmar Schulz Berlin [u.a.] Springer 1990 XV, 123 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1445 Quasielliptische Differentialgleichung (DE-588)4247394-9 gnd rswk-swf Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd rswk-swf Quasilineares elliptisches System (DE-588)4121544-8 gnd rswk-swf Regularität (DE-588)4049074-9 gnd rswk-swf Monge-Ampère-Differentialgleichung (DE-588)4253327-2 s DE-604 Regularität (DE-588)4049074-9 s Quasilineares elliptisches System (DE-588)4121544-8 s Quasielliptische Differentialgleichung (DE-588)4247394-9 s Lecture notes in mathematics 1445 (DE-604)BV000676446 1445 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002545042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schulz, Friedmar 1952- Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions Lecture notes in mathematics Quasielliptische Differentialgleichung (DE-588)4247394-9 gnd Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd Quasilineares elliptisches System (DE-588)4121544-8 gnd Regularität (DE-588)4049074-9 gnd |
| subject_GND | (DE-588)4247394-9 (DE-588)4253327-2 (DE-588)4121544-8 (DE-588)4049074-9 |
| title | Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions |
| title_auth | Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions |
| title_exact_search | Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions |
| title_full | Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions Friedmar Schulz |
| title_fullStr | Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions Friedmar Schulz |
| title_full_unstemmed | Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions Friedmar Schulz |
| title_short | Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions |
| title_sort | regularity theory for quasilinear elliptic systems and monge ampere equations in two dimensions |
| topic | Quasielliptische Differentialgleichung (DE-588)4247394-9 gnd Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd Quasilineares elliptisches System (DE-588)4121544-8 gnd Regularität (DE-588)4049074-9 gnd |
| topic_facet | Quasielliptische Differentialgleichung Monge-Ampère-Differentialgleichung Quasilineares elliptisches System Regularität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002545042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT schulzfriedmar regularitytheoryforquasilinearellipticsystemsandmongeampereequationsintwodimensions |