Introduction to the theory of nonlinear elliptic equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Leipzig
Teubner
1983
|
| Edition: | 1. Aufl. |
| Series: | Teubner-Texte zur Mathematik
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 204 S. |
| ISSN: | 0138-502X |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to the theory of nonlinear elliptic equations |c Jindřich Nečas |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Leipzig |b Teubner |c 1983 | |
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Record in the Search Index
| _version_ | 1804117790917918720 |
|---|---|
| adam_text | CONTENTS
CHAPTER 1 . THE TOPIC OF THE LECTURE NOTES AND SOMETHING ON
MODELLING BY PARTIAL DIFFERENTIAL EQUATIONS 6
1.1 Introduction 6
1.2 Partial differential equations in modelling 10
CHAPTER 2. SOBOLEV AND MORREY CAMPANATO SPACES 20
2.1 Definition of the Sobolev spaces 20
2.2 Imbedding theorems for Sobolev spaces 25
2.3 Complete continuity of imbedding 29
2.4 Traces 31
2.5 Poincare inequality 34
2.6 Morrey Campanato spaces 35
CHAPTER 3. EXISTENCE OF WEAK SOLUTIONS TO BOUNDARY VALUE
PROBLEMS FOR NONLINEAR SECOND ORDER ELLIPTIC
SYSTEMS 39
3.1 Weak solution 39
3.2 Variatlonal approach 45
3.3 The application of the theory of monotone
operators 53
3.4 Weakly coercive operators, the Fredholm alternative 63
3.5 Problems with asymptotes in resonance 69
CHAPTER 4. AN EXCURSION TO APROXIMATE METHODS 85
4.1 The Galerkin Ritz method 85
4.2 Method of steepest descent 87
4.3 The Newton method 88
4.4 Differentiate homotopy 95
4.5 Secant modulus method 101
CHAPTER 5. INTERMEDIARY REGULARITY 105
5.1 Introductory remarks 105
5.2 Estimates in the space W2 2 105
5.3 Estimates in the space W1 119
5.4 Maximum principle and the Liouville theorem,
m = 1 129
4
5.5 Estimate of sup|vu(x)| in virtue of the bounded
slope condition 135
CHAPTER 6. REGULARITY OF WEAK SOLUTIONS TO SECOND ORDER
ELLIPTIC SYSTEMS 138
6.1 Introduction 138
6.2 Partial regularity for quasilinear systems and
fundamental lemmas 142
6.3 Partial regularity for nonlinear elliptic systems
and regularity in the interior; condition of the
Liouville type L(Rn) 151
6.4 A counter example 156
6.5 The dimension n = 2 , one equation of the second
order, Saint Venant*s principle 159
6.6 Regularity up to the boundary via the fourth order
differential 164
6.7 A brief introduction to the theory of isotropic
polyconvex functionals in finite elasticity and
the regularity of solutions for special materials 171
6.8 Nonlinear elasticity 184
6.9 The regularity up to the boundary, conditions of
the Liouville type L(R ) 189
REFERENCES 199
5
|
| any_adam_object | 1 |
| author | Nečas, Jindřich 1929-2002 |
| author_GND | (DE-588)172282470 |
| author_facet | Nečas, Jindřich 1929-2002 |
| author_role | aut |
| author_sort | Nečas, Jindřich 1929-2002 |
| author_variant | j n jn |
| building | Verbundindex |
| bvnumber | BV003443234 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 |
| callnumber-search | QA1 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)10941042 (DE-599)BVBBV003443234 |
| dewey-full | 515.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
| dewey-search | 515.3/53 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| id | DE-604.BV003443234 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:00:00Z |
| institution | BVB |
| issn | 0138-502X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002179632 |
| oclc_num | 10941042 |
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| owner_facet | DE-384 DE-703 DE-739 DE-824 DE-29T DE-634 DE-11 DE-83 |
| physical | 204 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Nečas, Jindřich 1929-2002 Verfasser (DE-588)172282470 aut Introduction to the theory of nonlinear elliptic equations Jindřich Nečas 1. Aufl. Leipzig Teubner 1983 204 S. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 52 0138-502X Differential equations, Elliptic Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s DE-604 Elliptische Differentialgleichung (DE-588)4014485-9 s 1\p DE-604 Nichtlineare Differentialgleichung (DE-588)4205536-2 s 2\p DE-604 Teubner-Texte zur Mathematik 52 (DE-604)BV000012607 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002179632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nečas, Jindřich 1929-2002 Introduction to the theory of nonlinear elliptic equations Teubner-Texte zur Mathematik Differential equations, Elliptic Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4014485-9 (DE-588)4310554-3 |
| title | Introduction to the theory of nonlinear elliptic equations |
| title_auth | Introduction to the theory of nonlinear elliptic equations |
| title_exact_search | Introduction to the theory of nonlinear elliptic equations |
| title_full | Introduction to the theory of nonlinear elliptic equations Jindřich Nečas |
| title_fullStr | Introduction to the theory of nonlinear elliptic equations Jindřich Nečas |
| title_full_unstemmed | Introduction to the theory of nonlinear elliptic equations Jindřich Nečas |
| title_short | Introduction to the theory of nonlinear elliptic equations |
| title_sort | introduction to the theory of nonlinear elliptic equations |
| topic | Differential equations, Elliptic Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| topic_facet | Differential equations, Elliptic Nichtlineare Differentialgleichung Elliptische Differentialgleichung Nichtlineare elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002179632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT necasjindrich introductiontothetheoryofnonlinearellipticequations |