Nonlinear elliptic and parabolic equations of the second order:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Dordrecht [u.a.]
Reidel
1987
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XIII, 462 S. |
| ISBN: | 9027722897 |
Internformat
MARC
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| 100 | 1 | |a Krylov, Nikolaj V. |d 1941- |e Verfasser |0 (DE-588)121699684 |4 aut | |
| 240 | 1 | 0 | |a Nelinejnye elliptičskie i paroboličeskie uravnenija vtorogo porjadka |
| 245 | 1 | 0 | |a Nonlinear elliptic and parabolic equations of the second order |c N. V. Krylov |
| 264 | 1 | |a Dordrecht [u.a.] |b Reidel |c 1987 | |
| 300 | |a XIII, 462 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 7 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Équations différentielles elliptiques | |
| 650 | 7 | |a Équations différentielles elliptiques |2 ram | |
| 650 | 4 | |a Équations différentielles hyperboliques | |
| 650 | 4 | |a Équations différentielles non linéaires | |
| 650 | 7 | |a Équations différentielles non linéaires |2 ram | |
| 650 | 7 | |a Équations différentielles paraboliques |2 ram | |
| 650 | 7 | |a équation 2ème ordre |2 inriac | |
| 650 | 7 | |a équation elliptique |2 inriac | |
| 650 | 7 | |a équation non linéaire |2 inriac | |
| 650 | 4 | |a Differential equations, Elliptic | |
| 650 | 4 | |a Differential equations, Hyperbolic | |
| 650 | 4 | |a Differential equations, Nonlinear | |
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Datensatz im Suchindex
| _version_ | 1804115242740875264 |
|---|---|
| adam_text | TABLE OF CONTENTS
EDITOR S PREFACE ix
PREFACE xi
CHAPTER 1 / Auxiliary Notions 1
1.1. Domains and Functional Spaces of Smooth Functions 1
1.2. The Sobolev Spaces, Measures, and Lattices 9
1.3. Conditional Existence Theorems for the Solution of
a Nonlinear Equation 14
1.4. Comments 21
CHAPTER 2 / Nonlinear Equations with Constant Coefficients in
the Whole Space 22
2.1. Constructing the Resolvent 22
2.2. The Existence Theorem for the Solution and the Estimates
of its Derivatives 30
2.3. Comments 38
CHAPTER 3 / A Priori Estimates in Lp for Solutions of Nonlinear
Elliptic and Parabolic Equations 40
3.1. Some Properties of X Concave Functions 40
3.2. Estimation of Solutions of Special Nonlinear Equations 49
3.3. The Aleksandrov Estimate 60
3.4. The Maximum Principle and the Uniqueness of a Solution
in the Sobolev Class 76
3.5. Passage to the Limit for Nonlinear Operators in the
Sobolev Class 87
3.6. Passage to the Limit for Nonlinear Operators in Classes
of Convex Functions 98
3.7. The Uniqueness of a Solution and the Comparison Theorems
for Nonlinear Operators in the Class of Convex Functions 111
3.8. Comments 114
CHAPTER 4 / A Priori Estimates in C for Solutions of Linear
and Nonlinear Equations 116
4.1. Research into Properties of Two Special Functions 116
4.2. The Harnack Inequality and the Holder Condition for
Solutions of Linear Equations with Measurable
Coefficients 130
4.3. The Holder Condition for Solutions of Simultaneous
Linear Inequalities 140
v
vi TABLE OF CONTENTS
4.4. The Holder Condition for Solutions of Elliptic and
Parabolic Equations near the Boundary 153
4.5. The Holder Condition for Solutions of Simultaneous Linear
Inequalities near the Boundary and Estimation of their
Normal Derivatives 170
4.6. The Holder Condition for Solutions of Some Degenerate
Linear Equations on the Boundary 179
4.7 Comments 196
CHAPTER 5 / A Priori Estimates in C for Solutions of Nonlinear
Equations 198
5.1. The Boundedness of and the Holder Condition for the
Derivatives of Solutions on the Boundary 198
5.2. The Estimates of the First Derivative with Respect to X 210
5.3. The Estimates of the Derivative with Respect to t 226
2 12
5.4. Estimation of the Solution in the Norms of C and W 231
5.5. The Estimates of u in the Norm of C 251
5.6. Discussion of the First Order Matching Conditions 265
5.7. Comments 269
CHAPTER 6 / Existence Theorems for Solutions of Nondegenerate
Equations 271
6.1. The Class F, the Uniqueness of a Solution, and the
Estimate of |u| 271
6.2. The Existence of a Solution for F 6 F. The First
Boundary Value Problem 282
6.3. The Existence of a Solution for F £ F in a Nonsmooth
Domain and Cauchy s Problem _ 291
6.4. The Existence of a Solution for F. Examples 297
6.5. The Existence of a Solution for F 6 F 305
6.6. Comments 310
CHAPTER 7 / Degenerate Nonlinear Equations in the Whole Space 312
7.1. Permutations of a Differential Operator with an Elliptic
Operator 312
7.2. A Priori Estimates of the First and the Second Derivatives 320
7.3. The Existence of a Solution in the Class of Concave
Functions 32?
7.4. The Existence of a Solution in the Class of Concave
Functions for the Normalized Bellman Equation 343
7.5. An Example of a One Dimensional Degenerate Equation 352
7.6. Comments 3 59
CHAPTER 8 / Degenerate Nonlinear Equations in a Domain 361
8.1. Equations with Constant Coefficients in a Ball and a
Circular Cylinder 361
8.2. Examples of Equations with Monge Ampere Operators, and
Other Examples 371
8.3. Interrelation Between the Equation in a Domain of a
Euclidean Space and the Equation on a Manifold 376
TABLE OF CONTENTS vii
8.4. Permutation of a Differential Operator with an Elliptic
Operator on a Manifold 381
8.5. The Estimates of the Derivatives of a Solution to a
Nonlinear Equation on a Manifold 386
8.6. The Estimates of the Second Mixed Derivatives on the
Boundary of a Domain 403
8.7. The Solvability of Equations Weakly Nondegenerate
Along the Normal 416
8.8. The Solvability of Degenerate Equations in a Domain 430
8.9. Comments 438
APPENDIX 1 / Proof of Lemma 4.1.6 440
APPENDIX 2 / Aleksandrov Busemann Feller Theorem 444
BIBLIOGRAPHY 453
INDEX 461
|
| any_adam_object | 1 |
| author | Krylov, Nikolaj V. 1941- |
| author_GND | (DE-588)121699684 |
| author_facet | Krylov, Nikolaj V. 1941- |
| author_role | aut |
| author_sort | Krylov, Nikolaj V. 1941- |
| author_variant | n v k nv nvk |
| building | Verbundindex |
| bvnumber | BV000791523 |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 |
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| callnumber-sort | QA 3377 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 |
| classification_tum | MAT 355f MAT 356f |
| ctrlnum | (OCoLC)17007460 (DE-599)BVBBV000791523 |
| 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 |
| format | Book |
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| id | DE-604.BV000791523 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:19:30Z |
| institution | BVB |
| isbn | 9027722897 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000495850 |
| oclc_num | 17007460 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-703 DE-739 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-83 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-703 DE-739 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-83 |
| physical | XIII, 462 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Reidel |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Krylov, Nikolaj V. 1941- Verfasser (DE-588)121699684 aut Nelinejnye elliptičskie i paroboličeskie uravnenija vtorogo porjadka Nonlinear elliptic and parabolic equations of the second order N. V. Krylov Dordrecht [u.a.] Reidel 1987 XIII, 462 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 7 Aus d. Russ. übers. Équations différentielles elliptiques Équations différentielles elliptiques ram Équations différentielles hyperboliques Équations différentielles non linéaires Équations différentielles non linéaires ram Équations différentielles paraboliques ram équation 2ème ordre inriac équation elliptique inriac équation non linéaire inriac Differential equations, Elliptic Differential equations, Hyperbolic Differential equations, Nonlinear Ordnung 2 (DE-588)4350619-7 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s DE-604 Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 s Elliptische Differentialgleichung (DE-588)4014485-9 s Ordnung 2 (DE-588)4350619-7 s 1\p DE-604 Parabolische Differentialgleichung (DE-588)4173245-5 s 2\p DE-604 Soviet series Mathematics and its applications 7 (DE-604)BV004708148 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000495850&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 | Krylov, Nikolaj V. 1941- Nonlinear elliptic and parabolic equations of the second order Équations différentielles elliptiques Équations différentielles elliptiques ram Équations différentielles hyperboliques Équations différentielles non linéaires Équations différentielles non linéaires ram Équations différentielles paraboliques ram équation 2ème ordre inriac équation elliptique inriac équation non linéaire inriac Differential equations, Elliptic Differential equations, Hyperbolic Differential equations, Nonlinear Ordnung 2 (DE-588)4350619-7 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| subject_GND | (DE-588)4350619-7 (DE-588)4014485-9 (DE-588)4455524-6 (DE-588)4173245-5 (DE-588)4310554-3 |
| title | Nonlinear elliptic and parabolic equations of the second order |
| title_alt | Nelinejnye elliptičskie i paroboličeskie uravnenija vtorogo porjadka |
| title_auth | Nonlinear elliptic and parabolic equations of the second order |
| title_exact_search | Nonlinear elliptic and parabolic equations of the second order |
| title_full | Nonlinear elliptic and parabolic equations of the second order N. V. Krylov |
| title_fullStr | Nonlinear elliptic and parabolic equations of the second order N. V. Krylov |
| title_full_unstemmed | Nonlinear elliptic and parabolic equations of the second order N. V. Krylov |
| title_short | Nonlinear elliptic and parabolic equations of the second order |
| title_sort | nonlinear elliptic and parabolic equations of the second order |
| topic | Équations différentielles elliptiques Équations différentielles elliptiques ram Équations différentielles hyperboliques Équations différentielles non linéaires Équations différentielles non linéaires ram Équations différentielles paraboliques ram équation 2ème ordre inriac équation elliptique inriac équation non linéaire inriac Differential equations, Elliptic Differential equations, Hyperbolic Differential equations, Nonlinear Ordnung 2 (DE-588)4350619-7 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| topic_facet | Équations différentielles elliptiques Équations différentielles hyperboliques Équations différentielles non linéaires Équations différentielles paraboliques équation 2ème ordre équation elliptique équation non linéaire Differential equations, Elliptic Differential equations, Hyperbolic Differential equations, Nonlinear Ordnung 2 Elliptische Differentialgleichung Nichtlineare parabolische Differentialgleichung Parabolische Differentialgleichung Nichtlineare elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000495850&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
| work_keys_str_mv | AT krylovnikolajv nelinejnyeellipticskieiparoboliceskieuravnenijavtorogoporjadka AT krylovnikolajv nonlinearellipticandparabolicequationsofthesecondorder |