Nonlinear elliptic partial differential equations: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham, Switzerland
Springer
[2018]
|
| Series: | Universitext
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 253 Seiten Illustrationen, Diagramme |
| ISBN: | 9783319783895 |
| ISSN: | 0172-5939 |
Staff View
MARC
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| 240 | 1 | 0 | |a Équations aux dérivées partielles elliptiques non linéaires |
| 245 | 1 | 0 | |a Nonlinear elliptic partial differential equations |b an introduction |c Hervé Le Dret |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2018] | |
| 264 | 4 | |c © 2018 | |
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| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Partial differential equations | |
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Calculus of Variations and Optimal Control; Optimization | |
| 650 | 4 | |a Functional Analysis | |
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| adam_text | Contents
1 A Brief Review of Real and Functional Analysis....................... 1
LI A Little Topological Uniqueness Trick............................. 1
1.2 Integration Theory and the Lebesgue Convergence Theorems....... 2
1.3 Convolution and Mollification..................................... 6
1.4 Distribution Theory.............................................. 10
1.5 Holder and Sobolev Spaces........................................ 12
1.6 Duality and Weak Convergences in Sobolev Spaces.................. 18
1.7 The Weak and Weak-Star Topologies................................ 21
1.8 Variational Formulations and Their Interpretation................ 26
1.9 Some Spectral Theory............................................. 30
Appendix: The Topologies of $ and ................................. 32
2 Fixed Point Theorems and Applications.................................. 47
2.1 Brouwer’s Fixed Point Theorem.................................... 47
2.2 The Schauder Fixed Point Theorems................................ 56
2.3 Solving a Model Problem Using a Fixed Point Method............... 62
2.4 Exercises of Chap. 2 ............................................ 67
3 Superposition Operators................................................ 69
3.1 Superposition Operators in LP(Q.)................................ 69
3.2 Young Measures................................................... 73
3.3 Superposition Operators in W1,p(£2) ........................... 78
3.4 Superposition Operators and Boundary Trace..................... 89
3.5 Exercises of Chap. 3 ........................................... 90
4 The Galerkin Method ................................................... 93
4.1 Solving the Model Problem by the Galerkin Method................. 93
4.2 A Problem Reminiscent of Fluid Mechanics......................... 97
4.3 Exercises of Chap. 4 ........................................... 109
5 The Maximum Principle, Elliptic Regularity, and Applications......... Ill
5.1 The Strong Maximum Principle.................................... Ill
5.2 The Weak Maximum Principle...................................... 120
IX
X
Contents
5.3 Elliptic Regularity Results...................................... 122
5.4 The Method of Super- and Sub-Solutions........................... 131
5.5 Exercises of Chap. 5 ............................................ 136
6 Calculus of Variations and Quasilinear Problems...................... 141
6.1 Lower Semicontinuity and Convexity............................. 142
6.2 Application to Scalar Quasilinear Elliptic Boundary
Value Problems................................................... 145
6.3 Calculus of Variations in the Vectorial Case, Quasiconvexity.... 150
6.4 Quasiconvexity: A Necessary Condition and a Sufficient
Condition........................................................ 155
6.5 Exercises of Chap. 6........................................... 160
Appendix: Weak Lower Semicontinuity Proofs.......................... 165
7 Calculus of Variations and Critical Points........................... 179
7.1 Why Look for Critical Points? ................................... 179
7.2 Ekeland’s Variational Principle.................................. 182
7.3 The Palais-Smale Condition....................................... 188
7.4 The Deformation Lemma.......................................... 194
7.5 The Min-Max Principle and the Mountain Pass Lemma................ 200
7.6 Exercises of Chap. 7 ........................................ 211
8 Monotone Operators and Variational Inequalities....................... 215
8.1 Monotone Operators, Definitions and First Properties ............ 215
8.2 Examples of Monotone Operators................................. 217
8.3 Variational Inequalities......................................... 219
8.4 Examples of Variational Inequalities............................. 226
8.5 Pseudo-Monotone Operators........................................ 231
8.6 Leray-Lions Operators............................................ 236
8.7 Exercises of Chap. 8 ............................................ 240
References................................................................ 245
Index
249
|
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| author | Le Dret, Hervé |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045112559 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:09:01Z |
| institution | BVB |
| isbn | 9783319783895 |
| issn | 0172-5939 |
| language | English |
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| physical | x, 253 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Le Dret, Hervé Verfasser (DE-588)1035525062 aut Équations aux dérivées partielles elliptiques non linéaires Nonlinear elliptic partial differential equations an introduction Hervé Le Dret Cham, Switzerland Springer [2018] © 2018 x, 253 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Universitext 0172-5939 Mathematics Functional analysis Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Functional Analysis Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-78390-1 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030502857&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Le Dret, Hervé Nonlinear elliptic partial differential equations an introduction Mathematics Functional analysis Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Functional Analysis Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| subject_GND | (DE-588)4310554-3 |
| title | Nonlinear elliptic partial differential equations an introduction |
| title_alt | Équations aux dérivées partielles elliptiques non linéaires |
| title_auth | Nonlinear elliptic partial differential equations an introduction |
| title_exact_search | Nonlinear elliptic partial differential equations an introduction |
| title_full | Nonlinear elliptic partial differential equations an introduction Hervé Le Dret |
| title_fullStr | Nonlinear elliptic partial differential equations an introduction Hervé Le Dret |
| title_full_unstemmed | Nonlinear elliptic partial differential equations an introduction Hervé Le Dret |
| title_short | Nonlinear elliptic partial differential equations |
| title_sort | nonlinear elliptic partial differential equations an introduction |
| title_sub | an introduction |
| topic | Mathematics Functional analysis Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Functional Analysis Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| topic_facet | Mathematics Functional analysis Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Functional Analysis Nichtlineare elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030502857&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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