Linear and quasilinear elliptic equations:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1968
|
| Schriftenreihe: | Mathematics in science and engineering
46 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331377&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus d. Russ. übers. |
| Umfang: | XVIII, 495 S. |
Internformat
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| 240 | 1 | 0 | |a Linejnye i kvazilinejnye uravnenija elliptičeskogo tipa |
| 245 | 1 | 0 | |a Linear and quasilinear elliptic equations |c Olga A. Ladyzhenskaya and Nina N. Ural'tseva |
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1968 | |
| 300 | |a XVIII, 495 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics in science and engineering |v 46 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Analiza - Parcialne diferencialne enačbe | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 355f 2001 A 22042 |
|---|---|
| DE-BY-TUM_katkey | 494462 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010433999 |
| _version_ | 1821935724877840384 |
| adam_text | Contents
PREFACE vii
1. INTRODUCTION 1
1. The Basic Notation and Terminology 1
2. Admissible Extensions of the Concept of Solution of
Linear and Quasilinear Equations 9
3. The Basic Results and Their Possible Development 27
2. AUXILIARY PROPOSITIONS 39
1. Some Simple Inequalities 39
2. Functions in the Class Wlm (Q) 41
3. Functions in the Classes W]n (Q) and Vlm (Q) 50
4. Other Auxiliary Propositions 56
5. Bounds for max|u(^)| 70
6. The Function Class S3m(a, M, 7, 6. — j 81
7. The Classes S),,,(2LJS ) and S0m (Q|JS ) 90
8. The Classes $i% 95
3. LINEAR EQUATIONS 106
1. Solvability of the Dirichlet Problem in the Spaces
Ct,, (2). / 2 107
2. Schauder s A Priori Estimate 116
3. The Solvability in C2, a (£) of Other Boundary Value
Problems 134
4. Generalized Solutions in W (Q). The First Fundamental
Inequality 138
5. Solvability of the First Boundary Value Problem in W^(Q) 149
6. The Second and Third Boundary Value Problems 160
7. Interior Estimates in L2 of the Second Derivatives of an
Arbitrary Function in Terms of the Values of an Elliptic
Operator Applied to It 162
XV
XVI CONTENTS
8. The Second Fundamental Inequality for Elliptic Operators 169
9. On the Solvability of the First Boundary Value Problem
in the Space W „ (L1) 183
10. Conditions Under Which Generalized Solutions in VC^ (2)
Belong to Wl(Q) 185
11. Other Ways of Proving the Second Fundamental Inequality 190
12. Conditions Under Which Generalized Solutions in W
Belong to Ci, afor / 2 193
13. The Boundedness of Generalized Solutions in W (2) 195
14. Conditions Under Which Generalized Solutions in w (2)
Belong to Co, * 201
15. Conditions for Boundedness of max | Vu | and ux I for
Generalized Solutions in W (2) 203
16. Diffraction Problems 205
17. The Case of Two Independent Variables 223
18. Two Dimensional Saddle Shaped Surfaces 238
4. QUASILINEAR EQUATIONS WITH PRINCIPAL PART IN
DIVERGENCE FORM 244
1. Bounded Generalized Solutions. Continuity in the Sense
of Holder 245
2. Uniqueness in the Small 254
3. A Bound for max| Vu | 258
4. A Bound for max | Vu Over the Entire Region Q 266
5. Generalized Second Order Derivatives 270
6. A Bound for the Norms | u |,, „, Where / 1 277
7. Bounds for the Maximum Absolute Values of Generalized
Solutions 285
8. Existence Theorems 291
5. VARIATIONAL PROBLEMS 318
1. Statement of the Problems 318
2. Finding Functions That Minimize the Functional / (u) 321
3. Finding a Bound for the Maximum Absolute Value of
Solutions of Variational Problems 327
4. Proof of Holderness of Generalized Solutions 331
5. The Theorem on Uniqueness in the Small of Generalized
Solutions 334
6. Further Investigation of the Differentiability Properties
of Generalized Solutions 335
6. QUASILINEAR EQUATIONS OF THE GENERAL FORM 338
1. A Bound for the Norm | u |,_ „ in Terms of the Norm | u |,, „ 339
2. A Bound for maxj Vu 349
CONTENTS XVII
3. Existence Theorems 370
4. Two Dimensional Problems 379
7. LINEAR SYSTEMS OF ELLIPTIC EQUATIONS 386
1. Generalized Solutions in Wl2 (U) 386
2. A Bound for max | uj 389
3. A Bound for |u |,, u 395
4. A Priori Bounds for | u |, B, and || u ;| 2 398
5. Solvability of the Problem (1.1), (1.3) in the Classes
Ct.. (U) 402
6. Differentiability Properties of Generalized Solutions 404
8. QUASILINEAR SYSTEMS 406
1. A Priori Bounds for the Norms I u !,_„_„, Where / 1, in
Terms of max |u. Vu I 407
j
2. A Bound for I u )„. a 409
3. The Energy Inequality and a Bound for max I Vu | on the
Boundary 413
4. A Bound for max | Vu | 417
a
5. Existence Theorems 420
9. OTHER DEVICES FOR OBTAINING BOUNDS FOR THE
HOLDER CONSTANTS FOR SOLUTIONS AND THEIR
DERIVATIVES 423
1. The Case of the Simplest Equation 425
2. Bounds on Holder Constants for Solutions of Equations
(Linear and Quasilinear) with Principal Part in
Divergence Form 429
3. Bounds on the Oscillations of the Derivatives of Solutions
of Equations with Principal Part in Divergence Form 442
4. Equations Not in Divergence Form 443
5. Moser s Method of Bounding lulls for Solutions of Linear
Equations 446
6. Nirenberg s Estimate 452
7. Morrey s Method for Finding a Bound for the Holder Constant
for Solutions of Two Dimensional Variational Problems 456
10. OTHER BOUNDARY VALUE PROBLEMS 459
1. Formulation of the Problems and the General Procedure
for Solving Them 459
XVIII CONTENTS
2. Quasilinear Equations with Principal Part in Divergence
Form 465
3. Quasilinear Systems 481
BIBLIOGRAPHY 484
INDEX 493
|
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| author | Ladyženskaja, Olʹga A. 1922-2004 Ural'ceva, Nina N. 1934- |
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| bvnumber | BV003662460 |
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| discipline | Mathematik |
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| id | DE-604.BV003662460 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:08:11Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002331377 |
| oclc_num | 439365053 |
| open_access_boolean | |
| owner | DE-384 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-703 DE-19 DE-BY-UBM DE-634 DE-83 DE-188 |
| owner_facet | DE-384 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-703 DE-19 DE-BY-UBM DE-634 DE-83 DE-188 |
| physical | XVIII, 495 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | Acad. Press |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spellingShingle | Ladyženskaja, Olʹga A. 1922-2004 Ural'ceva, Nina N. 1934- Linear and quasilinear elliptic equations Mathematics in science and engineering Analiza - Parcialne diferencialne enačbe Lineare Differentialgleichung (DE-588)4206889-7 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Quasilineare elliptische Differentialgleichung (DE-588)4431553-3 gnd Elliptische Funktion (DE-588)4134665-8 gnd |
| subject_GND | (DE-588)4206889-7 (DE-588)4014485-9 (DE-588)4431553-3 (DE-588)4134665-8 |
| title | Linear and quasilinear elliptic equations |
| title_alt | Linejnye i kvazilinejnye uravnenija elliptičeskogo tipa |
| title_auth | Linear and quasilinear elliptic equations |
| title_exact_search | Linear and quasilinear elliptic equations |
| title_full | Linear and quasilinear elliptic equations Olga A. Ladyzhenskaya and Nina N. Ural'tseva |
| title_fullStr | Linear and quasilinear elliptic equations Olga A. Ladyzhenskaya and Nina N. Ural'tseva |
| title_full_unstemmed | Linear and quasilinear elliptic equations Olga A. Ladyzhenskaya and Nina N. Ural'tseva |
| title_short | Linear and quasilinear elliptic equations |
| title_sort | linear and quasilinear elliptic equations |
| topic | Analiza - Parcialne diferencialne enačbe Lineare Differentialgleichung (DE-588)4206889-7 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Quasilineare elliptische Differentialgleichung (DE-588)4431553-3 gnd Elliptische Funktion (DE-588)4134665-8 gnd |
| topic_facet | Analiza - Parcialne diferencialne enačbe Lineare Differentialgleichung Elliptische Differentialgleichung Quasilineare elliptische Differentialgleichung Elliptische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331377&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001196 |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 355f 2001 A 22042 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |