Geometrical methods in variational problems:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1999
|
| Series: | Mathematics and its applications
485 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 539 S. |
| ISBN: | 0792357809 |
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| 245 | 1 | 0 | |a Geometrical methods in variational problems |c by N. A. Bobylev, S. V.Emel'yanov and S. K. Korovin |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1999 | |
| 300 | |a XVI, 539 S. | ||
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| 490 | 1 | |a Mathematics and its applications |v 485 | |
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Record in the Search Index
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| adam_text | GEOMETRICAL METHODS IN VARIATIONAL PROBLEMS BY N. A. BOBYLEV INSTITUTE
FOR CONTROL PROBLEMS, MOSCOW, RUSSIA S. V. EMEL YANOV INSTITUTE OF
SYSTEMS ANALYSIS, MOSCOW, RUSSIA AND S. K. KOROVIN M. V. LOMONOSOV
MOSCOW STATE UNIVERSITY, MOSCOW, RUSSIA KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON CONTENTS 1 PRELIMINARIES 1 1.1 METRIC AND
NORMED SPACES 1 1.1.1 METRIC SPACES 1 1.1.2 LINEAR SPACES 2 1.1.3 LINEAR
NORMED SPACES AND BANACH SPACES 4 1.1.4 HILBERT SPACES 4 1.1.5 SPECIFIC
FUNCTION SPACES * 5 1.2 COMPACTNESS 8 1.2.1 COMPACT SETS 8 1.2.2
COMPACTNESS CRITERIA IN FUNCTION SPACES 9 1.3 LINEAR FUNCTIONAL AND DUAL
SPACES 10 1.3.1 LINEAR FUNCTIONALS 10 1.3.2 HAHN-BANACH THEOREM 11 1.3.3
DUAL SPACE 11 1.3.4 REFLEXIVE SPACES 12 1.3.5 WEAK CONVERGENCE 12 1.3.6
WEAK COMPACTNESS 13 1.4 LINEAR OPERATORS 14 1.4.1 DEFINITIONS 14 1.4.2
CONVERGENCE OF LINEAR OPERATORS 15 1.4.3 INVERSE OPERATORS 15 1.4.4
UNBOUNDED OPERATORS 16 1.4.5 CLOSED GRAPH THEOREM 16 1.4.6 SPECTRUM OF A
LINEAR OPERATOR 17 1.4.7 ADJOINT OPERATORS 17 L4.8 SPACE OF LINEAR
OPERATORS 18 1.4.9 COMPLETELY CONTINUOUS OPERATORS 18 1.4.10 EMBEDDING
OPERATORS 18 1.4.11 LINEAR INTEGRAL OPERATORS 19 1.5 NONLINEAR OPERATORS
AND FUNCTIONALS 21 1.5.1 CONTINUITY 21 1.5.2 DIFFERENTIABILITY 22 1.5.3
LIPSCHITZ AND CONVEX FUNCTIONALS 25 1.5.4 SPECIFIC NONLINEAR OPERATORS
AND THEIR PROPERTIES . . 30 1.5.5 EXTENSION OF MAPPINGS AND THE THEOREM
ON THE PAR- TITION OF UNITY ** 31 1.6 CONTRACTION MAPPING PRINCIPLE,
IMPLICIT FUNCTION THEOREM, AND DIFFERENTIAL EQUATIONS ON A BANACH SPACE
32 1.6.1 CONTRACTION MAPPINGS 33 1.6.2 IMPLICIT FUNCTION THEOREM 33 VI
1.6.3 CAUCHY PROBLEM 34 2 MINIMIZATION OF NONLINEAR FUNCTIONALS 37 2.1
EXTREMA OF SMOOTH FUNCTIONALS . 37 2.1.1 CRITICAL POINTS 37 2.1.2 SECOND
ORDER NECESSARY CONDITIONS FOR MINIMUM ... 38 2.1.3 CONVEX FUNCTIONALS
39 2.1.4 GLOBAL MINIMUM OF SMOOTH FUNCTIONALS 40 2.1.5 CONDITIONAL
EXTREMUM 46 2.2 EXTREMUM OF LIPSCHITZIAN AND CONVEX FUNCTIONALS 51 2.2.1
DISTANCE FUNCTIONAL 51 2.2.2 TANGENT AND NORMAL CONES 52 2.2.3 CRITICAL
POINTS OF LIPSCHITZIAN FUNCTIONALS 53 2.2.4 CONDITIONALLY CRITICAL
POINTS OF LIPSCHITZIAN FUNCTIONALS 53 2.3 WEIERSTASS THEOREMS 54 2.3.1
CONTINUOUS FUNCTIONALS 55 2.3.2 SEMICONTINUOUS FUNCTIONALS 55 2.3.3
WEAKLY SEMICONTINUOUS FUNCTIONALS 56 2.3.4 GROWING FUNCTIONALS 58 2.3.5
CONVEX FUNCTIONALS 59 2.4 MONOTONICITY 61 2.4.1 DEFINITIONS 61 2.4.2
POTENTIAL OPERATORS 62 2.4.3 MONOTONICITY AND CONVEXITY 63 2.5
VARIATIONAL PRINCIPLES 65 2.5.1 EKELAND THEOREM 65 2.5.2 FUNCTIONALS ON
BANACH AND HILBERT SPACES 68 - 2.5.3 COUNTEREXAMPLE 71 2.6 ADDITIONAL
REMARKS 72 2.6.1 STABILITY OF THE EQUILIBRIUM STATE OF AUTONOMOUS SYS-
TEMS 72 2.6.2 BORWEIN-PREISS AND DE VILLE VARIATIONAL PRINCIPLES . 73
2.6.3 CONSTRUCTIVE VARIATIONAL PRINCIPLE BY IOFFE-TIKHOMIROV 75 3
HOMOTOPIC METHODS IN VARIATIONAL PROBLEMS 79 3.1 DEFORMATIONS OF
FUNCTIONALS ON HILBERT SPACES 79 3.1.1 //-REGULAR FUNCTIONALS 79 3.1.2
DEFORMATION PRINCIPLE OF MINIMUM 79 3.1.3 PREPARATORY LEMMAS 80 3.1.4
PROOF OF THE MAIN THEOREM 82 3.1.5 ON THE PROPERTY OF ^-REGULARITY 86
VLL 3.2 DEFORMATIONS OF FUNCTIONALS ON BANACH SPACES 87 3.2.1 .E-REGULAR
FUNCTIONALS 87 3.2.2 PREPARATORY LEMMAS 87 3.2.3 PROOF OF THE
DEFORMATION THEOREM 93 3.3 GLOBAL DEFORMATIONS OF FUNCTIONALS 94 3.3.1 A
COUNTEREXAMPLE 94 3.3.2 GLOBAL DEFORMATIONS 95 3.3.3 GENERALIZATIONS 96
3.4 DEFORMATION OF PROBLEMS OF THE CALCULUS OF VARIATIONS ... 97 3.4.1
ONE-DIMENSIONAL PROBLEMS 97 3.4.2 HIGHER-DIMENSIONAL INTEGRAL
FUNCTIONALS 99 3.4.3 DEFORMATION THEOREM 100 3.4.4 DEFORMATIONS OF
INTEGRAL FUNCTIONALS IN THE PROBLEM ON A WEAK MINIMUM ^ 101 3.5
DEFORMATIONS OF LIPSCHITZIAN FUNCTIONS 110 3.5.1 GENERALIZED DERIVATIVE
AND THE GENERALIZED GRADIENT . 110 3.5.2 DEFORMATION THEOREM 110 3.6
GLOBAL DEFORMATIONS OF LIPSCHITZIAN FUNCTIONS 115 3.6.1 PREPARATORY
LEMMAS 115 3.6.2 DEFORMATION THEOREM 119 3.6.3 LINEAR DEFORMATIONS 120
3.7 DEFORMATIONS OF MATHEMATICAL PROGRAMMING PROBLEMS ... 121 3.7.1
EXTREMALS OF LIPSCHITZIAN NONLINEAR PROGRAMMING PROB- LEMS 121 3.7.2
EXTREMALS OF CLASSICAL NONLINEAR PROGRAMMING PROBLEMS 122 3.7.3
DEFORMATION THEOREM 123 3.7.4 LINEAR DEFORMATIONS OF NONLINEAR
PROGRAMMING PROB- LEMS AND THE INVARIANCE OF THE GLOBAL MINIMUM . . .
130 3.8 DEFORMATIONS OF LIPSCHITZIAN FUNCTIONALS 132 3.8.1 (P,
5)-REGULAR FUNCTIONALS 132 3.8.2 DEFORMATION THEOREM 132 3.8.3
PREPARATORY LEMMAS 133 3.8.4 PROOF OF THE DEFORMATION THEOREM 136 3.9
ADDITIONAL REMARKS 138 3.9.1 DEFORMATIONS OF INFINITE-DIMENSIONAL
MATHEMATICAL PRO- GRAMMING PROBLEMS 139 3.9.2 DEFORMATIONS OF
MULTICRITERIA PROBLEMS 140 3.9.3 MULTICRITERIA PROBLEMS WITH CONSTRAINTS
142 3.9.4 DEFORMATION PRINCIPLE OF MINIMUM FOR FUNCTIONALS ON METRIC
SPACES 144 3.9.5 NORMAL DEFORMATIONS 145 3.9.6 INVERSION OF DEFORMATION
THEOREMS 147 VLLL 3.9.7 ON DIFFERENTIABILITY OF INTEGRAL FUNCTIONALS 149
3.9.8 HOMOTOPY INVARIANCE OF THE CONLEY INDEX 153 4 TOPOLOGICAL
CHARACTERISTICS OF EXTREMALS OF VARIATIONAL PROBLEMS 155 4.1 SMOOTH
MANIFOLDS AND DIFFERENTIAL FORMS 155 4.1.1 MANIFOLDS WITHOUT BOUNDARY
155 4.1.2 TANGENT SPACES 156 4.1.3 ORIENTATION 158 4.1.4 MANIFOLDS WITH
BOUNDARY 158 4.1.5 EXTERIOR FORMS 160 4.1.6 EXTERIOR PRODUCT 160 4.1.7
DIFFERENTIAL FORMS 161 4.1.8 INTEGRATION OF DIFFERENTIAL FORMS 162 4.1.9
EXTERIOR DIFFERENTIATION 163 4.2 DEGREE OF MAPPING 164 4.2.1 SARD
THEOREM 164 4.2.2 LEMMAS ON ONE-DIMENSIONAL MANIFOLDS 165 4.2.3 DEGREE
OF MAPPING 167 4.2.4 DEGREE OF MAPPING (SECOND APPROACH) 171 4.2.5
CONNECTIONS BETWEEN TWO DEFINITIONS OF THE DEGREE OF MAPPING 175 4.2.6
PROPERTIES OF DEGREE OF MAPPING 175 4.2.7 DEGREE OF CONTINUOUS MAPPINGS
179 4.2.8 HOPF THEOREM 180 4.3 ROTATION OF VECTOR FIELDS IN
FINITE-DIMENSIONAL SPACES . . . 180 4.3.1 VECTOR FIELDS 180 4.3.2
HOMOTOPIC VECTOR FIELDS 180 4.3.3 ROTATION OF VECTOR FIELDS 181 4.3.4
PROPERTIES OF ROTATION 182 4.4 VECTOR FIELDS IN INFINITE-DIMENSIONAL
SPACES 193 4.4.1 COMPLETELY CONTINUOUS VECTOR FIELDS 193 4.4.2 MONOTONE
VECTOR FIELDS 201 4.4.3 MULTIVALUED VECTOR FIELDS 208 4.5 COMPUTATION OF
THE TOPOLOGICAL INDEX 216 4.5.1 LINEARIZABLE FIELDS 216 4.5.2
COMPUTATION OF THE TOPOLOGICAL INDEX OF A DEGENERATE ZERO 218 4.5.3 ODD
FIELDS 221 4.6 TOPOLOGICAL INDEX OF ZERO OF AN ISOLATED MINIMUM 223
4.6.1 FUNCTIONALS ON HILBERT SPACES 223 4.6.2 FUNCTIONALS ON BANACH
SPACES 227 IX 4.6.3 CONDITIONAL EXTREMUM 228 4.7 EULER CHARACTERISTIC
AND THE TOPOLOGICAL INDEX OF AN ISO- LATED CRITICAL SET 230 4.7.1 EULER
CHARACTERISTIC 230 4.7.2 TOPOLOGICAL INDEX OF THE MANIFOLD OF MINIMA . .
. . 231 4.7.3 GROWING FUNCTIONALS 234 4.8 TOPOLOGICAL INDEX OF EXTREMALS
OF PROBLEMS OF THE CALCULUS OF VARIATIONS 235 4.8.1 ONE-DIMENSIONAL
PROBLEMS 235 4.8.2 HIGH-DIMENSIONAL INTEGRAL FUNCTIONALS 238 4.8.3
TOPOLOGICAL INDEX OF EXTREMALS OF HIGHER-DIMENSIONAL VARIATIONAL
PROBLEMS WITH STRONG NONLINEARITIES . . . 238 4.9 TOPOLOGICAL INDEX OF
OPTIMAL CONTROLS 242 4.9.1 STATEMENT OF THE PROBLEM 242 4.9.2 AUXILIARY
RESULTS 243 4.9.3 NECESSARY OPTIMALITY CONDITION 249 4.10 TOPOLOGICAL
CHARACTERISTIC S OF CRITICAL POINTS OF NONSMOOTH FUNCTIONALS 251 4.10.1
FUNCTIONS OF A FINITE NUMBER OF VARIABLES 251 4.11 ADDITIONAL REMARKS
260 4.11.1 LIPSCHITZIAN FUNCTIONALS 260 4.11.2 CRITICAL POINTS OF
FUNCTIONALS AND THE LYUSTERNIK- SHNIREL MAN THEORY 263 4.11.3
TOPOLOGICAL INDEX OF ZERO OF A MONOTONE VECTOR FIELD 267 APPLICATIONS
269 5.1 EXISTENCE THEOREMS 269 5.1RL ABSTRACT THEOREMS 269 5.1.2
GENERALIZED SOLUTIONS TO BOUNDARY-VALUE PROBLEMS FOR ELLIPTIC EQUATIONS
271 5.1.3 EXISTENCE OF SOLUTIONS TO THE HAMMERSTEIN EQUATION 276 5.1.4
PROBLEM OF THE ELASTIC-PLASTIC TWISTING OF STRENGTH- ENING RODS 279
5.1.5 PROBLEM OF ELASTIC-PLASTIC BEND OF A PLATE 282 5.1.6
GINZBURG-LANDAU EQUATIONS 284 5.1.7 SOLVABILITY OF NONVARIATIONAL
PROBLEMS 288 5.1.8 PROBLEM OF STRONG BENDING OF THIN PLATES 289 5.1.9
STATIONARY NAVIER-STOKES PROBLEM 292 5.2 BOUNDS OF THE NUMBER OF
SOLUTIONS TO VARIATIONAL PROBLEMS 294 5.2.1 MOUNTAIN-PASS THEOREM 294
5.2.2 GUIDE-NONEQUIVALENT SOLUTIONS TO THE GINZBURG-LANDAU EQUATIONS 295
5.2.3 ESTIMATION OF THE NUMBER OF SOLUTIONS TO THE PROBLEM OF THE STRONG
BENDING OF THIN PLATES 297 5.2.4 POINCARE THEOREM 300 5.2.5 PERIODIC
OSCILLATION IN POTENTIAL SYSTEMS 301 5.3 APPLICATIONS OF THE HOMOTOPIC
METHOD 304 5.3.1 PROOF OF INEQUALITIES (GENERAL PRINCIPLES) 305 5.3.2
SYLVESTER CRITERION 306 5.3.3 YOUNG INEQUALITY 309 5.3.4 MINKOWSKI
INEQUALITY 310 5.3.5 JENSEN INEQUALITY 312 5.3.6 CAUCHY INEQUALITY
(INEQUALITY BETWEEN THE ARITHMETI- CAL MEAN AND THE GEOMETRICAL MEAN)
313 5.3.7 IMPROVEMENTS AND GENERALIZATIONS OF THE CAUCHY IN- EQUALITY
314 5.3.8 FUNCTIONAL INEQUALITIES 316 5.3.9 SOLVABILITY OF BOUNDARY
VALUE PROBLEMS AND TESTS FOR MINIMUM OF INTEGRAL FUNCTIONALS 319 5.3.10
EXAMINING THE MINIMALITY OF EXTREMALS 322 5.3.11 SUFFICIENT CONDITION
FOR MINIMUM IN NONLINEAR PRO- GRAMMING PROBLEMS 323 5.4 STUDY OF
DEGENERATE EXTREMALS 328 5.4.1 REGULARLY DEGENERATE CRITICAL POINTS 328
5.4.2 DIMENSION REDUCTION PRINCIPLE 330 5.4.3 ANALYSIS OF ZERO POINTS OF
THE SPECTRUM OF THE SECOND VARIATION 333 5.4.4 (,//)-REGULAR
FUNCTIONALS 335 5.4.5 JACOBI THEOREMS 338 ,-5.4.6 DIMENSION REDUCTION
PRINCIPLE FOR FUNCTIONALS ON BA- NACH SPACES 340 5.4.7 DEGENERATE
EXTREMALS OF HIGHER-DIMENSIONAL VARIATIONAL PROBLEMS 346 5.4.8
TOPOLOGICAL INDEX AND SUFFICIENT CONDITIONS FOR EX- TREMUM 351 5.5 MORSE
LEMMAS 358 5.5.1 FINITE-DIMENSIONAL MORSE LEMMA 359 5.5.2 MORSE LEMMA
FOR SMOOTH FUNCTIONALS ON HILBERT SPACES359 5.5.3 MORSE LEMMAS FOR
FUNCTIONALS ON BANACH SPACES . . 362 5.5.4 PARAMETRIC MORSE LEMMA 368
5.5.5 MORSE LEMMAS FOR FUNCTIONALS OF THE CALCULUS OF VARI- ATIONS 372
5.6 WELL-POSEDNESS OF VARIATIONAL PROBLEMS. ULAM PROBLEM . . 376 5.6.1
TIKHONOV WELL-POSEDNESS 377 XI 5.6.2 WEAK CONVERGENCE OF MINIMIZING
SEQUENCES 379 5.6.3 STABILITY OF CRITICAL POINTS IN FINITE-DIMENSIONAL
SPACES 379 5.6.4 ULAM PROBLEM 380 5.7 GRADIENT PROCEDURES 395 5.7.1
GENERAL FACTS 395 5.7.2 CONVEX FUNCTIONALS 396 5.7.3 STEEPEST DESCENT
METHOD FOR //-REGULAR FUNCTIONALS 402 5.7.4 GRADIENT METHOD FOR (P,
5)-REGULAR FUNCTIONALS . . . 405 5.7.5 FUNCTIONALS OF THE CLASSICAL
CALCULUS OF VARIATIONS . . 410 5.7.6 HIGHER-DIMENSIONAL VARIATIONAL
PROBLEMS 412 5.7.7 GRADIENT PROJECTION METHOD 414 5.7.8 GRADIENT
PROJECTION METHOD IN PROBLEMS OF THE CAL- CULUS OF VARIATIONS 424 5.7.9
CONTROL PROBLEMS OF DYNAMICAL SYSTEMS 425 5.7.10 OPTIMAL CONTROL
PROBLEMS OF DISTRIBUTED PARAMETER SYSTEMS 428 5.8 BIFURCATION OF
EXTREMALS OF VARIATIONAL PROBLEMS 431 5.8J NECESSARY CONDITION FOR
BIFURCATION 431 5.8.2 EXISTENCE OF BIFURCATION POINTS 432 5.8.3 ANALYSIS
OF BIFURCATION VALUES OF PARAMETERS . . . . 434 5.8.4 PROBLEM OF THE
LOSS OF STABILITY OF THIN PLATES . . . . 449 5.9 EIGENVALUES OF
POTENTIAL OPERATORS 450 5.9.1 WEAKLY CONTINUOUS FUNCTIONALS 450 5.9.2
EVEN WEAKLY CONTINUOUS FUNCTIONALS 452 5.9.3 GENUS OF SETS 453 5.9.4
LEMMAS ON WEAKLY CONTINUOUS FUNCTIONALS 457 5.9.5 PROOF OF THE THEOREM
ON EIGENVECTORS 463 .5.9.6 STABILITY OF CRITICAL VALUES 464 5.9.7 SMALL
PERTURBATIONS OF EVEN FUNCTIONALS 470 5.10 ADDITIONAL REMARKS 470 5.10.1
BIFURCATION OF EXTREMALS OF (E, //)-REGULAR FUNCTIONALS 470 5.10.2
BIFURCATION OF EXTREMALS OF VARIATIONAL PROBLEMS WITH STRONG
NONLINEARITIES 472 5.10.3 MORSE LEMMAS FOR HIGHER-DIMENSIONAL
VARIATIONAL PROB- LEMS 473 5.10.4 EIGENVECTORS OF POTENTIAL OPERATORS ON
ORLICZ-SOBOLEV SPACES 475 5.10.5 GENUS OF SETSHN BANACH SPACES 482
5.10.6 DUAL VARIATIONAL PRINCIPLE AND PERIODIC SOLUTIONS TO HAMILTONIAN
SYSTEMS 485 5.10.7 GRADIENT PROCEDURES IN PROBLEMS WITH NONISOLATED
EXTREMALS 491 XLL 5.10.8 CONVERGENCE OF GRADIENT PROCEDURES IN UNIFORM
NORMS493 5.10.9 OPEN PROBLEMS 492 BIBLIOGRAPHICAL COMMENTS 497
REFERENCES 507 INDEX 535
|
| any_adam_object | 1 |
| author | Bobylev, Nikolaj A. Emelʹjanov, Stanislav V. 1929- Korovin, Sergej K. 1945- |
| author_GND | (DE-588)121848981 (DE-588)121849007 |
| author_facet | Bobylev, Nikolaj A. Emelʹjanov, Stanislav V. 1929- Korovin, Sergej K. 1945- |
| author_role | aut aut aut |
| author_sort | Bobylev, Nikolaj A. |
| author_variant | n a b na nab s v e sv sve s k k sk skk |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 660 |
| classification_tum | MAT 490f |
| ctrlnum | (OCoLC)41238463 (DE-599)BVBBV013671571 |
| dewey-full | 515/.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.64 |
| dewey-search | 515/.64 |
| dewey-sort | 3515 264 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013671571 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:56Z |
| institution | BVB |
| isbn | 0792357809 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009340416 |
| oclc_num | 41238463 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-634 DE-11 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-634 DE-11 |
| physical | XVI, 539 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Bobylev, Nikolaj A. Verfasser aut Geometrical methods in variational problems by N. A. Bobylev, S. V.Emel'yanov and S. K. Korovin Dordrecht [u.a.] Kluwer Acad. Publ. 1999 XVI, 539 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 485 Variational inequalities (Mathematics) Geometrische Methode (DE-588)4156715-8 gnd rswk-swf Variationsproblem (DE-588)4187419-5 gnd rswk-swf Variationsproblem (DE-588)4187419-5 s Geometrische Methode (DE-588)4156715-8 s DE-604 Emelʹjanov, Stanislav V. 1929- Verfasser (DE-588)121848981 aut Korovin, Sergej K. 1945- Verfasser (DE-588)121849007 aut Mathematics and its applications 485 (DE-604)BV008163334 485 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009340416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bobylev, Nikolaj A. Emelʹjanov, Stanislav V. 1929- Korovin, Sergej K. 1945- Geometrical methods in variational problems Mathematics and its applications Variational inequalities (Mathematics) Geometrische Methode (DE-588)4156715-8 gnd Variationsproblem (DE-588)4187419-5 gnd |
| subject_GND | (DE-588)4156715-8 (DE-588)4187419-5 |
| title | Geometrical methods in variational problems |
| title_auth | Geometrical methods in variational problems |
| title_exact_search | Geometrical methods in variational problems |
| title_full | Geometrical methods in variational problems by N. A. Bobylev, S. V.Emel'yanov and S. K. Korovin |
| title_fullStr | Geometrical methods in variational problems by N. A. Bobylev, S. V.Emel'yanov and S. K. Korovin |
| title_full_unstemmed | Geometrical methods in variational problems by N. A. Bobylev, S. V.Emel'yanov and S. K. Korovin |
| title_short | Geometrical methods in variational problems |
| title_sort | geometrical methods in variational problems |
| topic | Variational inequalities (Mathematics) Geometrische Methode (DE-588)4156715-8 gnd Variationsproblem (DE-588)4187419-5 gnd |
| topic_facet | Variational inequalities (Mathematics) Geometrische Methode Variationsproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009340416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT bobylevnikolaja geometricalmethodsinvariationalproblems AT emelʹjanovstanislavv geometricalmethodsinvariationalproblems AT korovinsergejk geometricalmethodsinvariationalproblems |