Convex analysis and nonlinear geometric elliptic equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1994
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 510 S. |
| ISBN: | 3540136207 0387136207 |
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MARC
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| 100 | 1 | |a Bakel'man, Il'ja Ja. |d 1928-1992 |e Verfasser |0 (DE-588)122949269 |4 aut | |
| 245 | 1 | 0 | |a Convex analysis and nonlinear geometric elliptic equations |c Ilya J. Bakelman |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
| 300 | |a XXI, 510 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804124239519809536 |
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| adam_text | ILYA J. BAKELMAN
CONVEX ANALYSIS
AND NONLINEAR GEOMETRIE
ELLIPTIC EQUATIONS
SPRINGER-VERLAG
BERLIN HEIDELBERG NEW YORK
LONDON PARIS TOKYO
HONGKONG BARCELONA
BUDAPEST
CONTENT
S
PAR
T I. ELEMENTS OF CONVEX ANALYSIS 1
CHAPTE
R 1. CONVE
X BODIE
S AND HYPERSURFACE
S 3
§!. CONVEX SETS IN FINITE-DIMENSIONAL EUCLIDEAN SPACES 3
1.1. MAIN DEFINITION 3
1.2. LINEAR AND CONVEX OPERATIONS WITH CONVEX SETS.
CONVEX HUELL 3
1.3. THE PROPERTIES OF CONVEX SETS IN LINEAR TOPOLOGICAL SPACES 7
1.4. EUCLIDEAN SPACE E
N
8
1.5. THE SIMPLE FIGURES IN E
N
9
1.6. SPHERICAL CONVEX SETS 10
1.7. STARSHAPEDNESS OF CONVEX BODIES 11
1.8. ASYMPTOTIC CONE 12
1.9. COMPLETE CONVEX HYPERSURFACES IN E
N+1
13
$2. SUPPORTING HYPERPLANES 14
2.1
. SUPPORTING HYPERPLANES. THE SEPARABILITY THEOREM 14
2.2. TH
E MAIN PROPERTIES OF SUPPORTING HYPERPLANES 15
§5. CONVEX HYPERSURFACES AND CONVEX FUNCTIONS 16
3.1. CONVEX HYPERSURFACES AND CONVEX FUNCTIONS 16
3.2. TEST OF CONVEXITY OF SMOOTH FUNCTIONS 19
3.3. CONVERGENCE OF CONVEX FUNCTIONS 20
3.4. CONVERGENCE IN TOPOLOGICAL SPACES 21
3.5. CONVERGENCE OF CONVEX BODIES AND CONVEX HYPERSURFACES 22
Y
. CONVEX POLYHEDRA 24
4.1
. DEFINITIONS. DESCRIPTION OF CONVEX POLYHEDRA BY TH
E CONVEX HUELL
OF THEIR VERTICES 24
4.2. CONVEX HUU OF A FINIT
E SYSTEM OF POINTS 26
4.3. APPROXIMATION OF CLOSED CONVEX HYPERSURFACES
BY CLOSED CONVEX POLYHEDRA 28
§5. INTEGRAL GAUSSIAN CURVATURE 29
5.1. SPHERICAL MAPPING AND TH
E INTEGRAL GAUSSIAN CURVATURE 29
5.2. THE CONVERGENCE OF INTEGRAL GAUSSIAN CURVATURES 33
5.3. INFINITE CONVEX HYPERSURFACES 35
§. SUPPORTING FUNCTION 36
6.1. DEFINITION AND MAIN PROPERTIES 36
6.2. DIFFERENTIAL GEOMETRY OF SUPPORTING FUNCTION 41
CHAPTE
R 2
. MIXE
D VOLUMES
.
MINKOWSK
I PROBLEM
. SELECTE
D GLOBA
L PROBLEM
S
IN GEOMETRI
E PARTIA
L DIFFERENTIAL EQUATION
S 54
XVI CONTENTS
§7. THE MINKOWSKI MIXED VOLUMES 54
7.1
. LINEA
R COMBINATION
S OF SET
S I
N E
+1
54
7.2. EXERCISE
S AN
D PROBLEM
S T
O SUBSECTIO
N 7.1 58
7.3
. MINKOWSK
I MIXED VOLUMES FOR CONVE
X POLYHEDR
A 59
7.4. TH
E MINKOWSKI MIXED VOLUMES
FOR GENERA
L BOUNDE
D CONVEX BODIE
S 6
3
7.5
. TH
E BRUNN-MINKOWSK
I THEOREM
.
TH
E MINKOWSKI INEQUALITIE
S 66
7.6. ALEXANDROV
S AN
D FENCHEPS INEQUALITIE
S 72
§8. SELECTED GLOBAL PROBLEMS
IN GEOMETRIE PARTIAL DIFFERENTIAL EQUATIONS 75
8.1
. MINKOWSKI S PROBLE
M FOR CONVEX POLYHEDR
A I
N ^
+
1
75
8.2. TH
E CLASSICAL MINKOWSKI THEORE
M 80
8.3
. GENERA
L ELLIPTI
C OPERATOR
S AN
D EQUATION
S 86
8.4. LINEAR ELLIPTI
C OPERATOR
S AN
D EQUATION
S 8
7
8.5. QUASILINEAR ELLIPTI
C OPERATOR
S AN
D EQUATION
S 88
8.6. TH
E CLASSICAL MONGE-AMPER
E EQUATION
S 89
8.7. DIFFERENTIAL EQUATION
S I
N GLOBA
L PROBLEM
S
OF DIFFERENTIAL GEOMETR
Y 90
8.8. TH
E CLASSICAL MAXIMU
M PRINCIPLE
S
FOR GENERAL ELLIPTI
C EQUATION
S 95
8.9. HOPF
S MAXIMU
M PRINCIPL
E FOR UNIFORML
Y ELLIPTI
C
LINEAR EQUATION
S 98
8.10. UNIQUENESS THEORE
M
FOR GENERA
L NONLINEA
R ELLIPTI
C EQUATION
S 100
8.11
. TH
E MAXIMU
M PRINCIPL
E
FOR DIVERGENT QUASILINEA
R ELLIPTI
C EQUATION
S 103
8.12. UNIQUENESS THEORE
M FOR ISOMETRI
C EMBEDDING
S
OF TWO-DIMENSIONA
L RIEMANNIA
N METRIC
S I
N E
3
105
PAR
T IL GEOMETRIE THEORY OF ELLIPTIC SOLUTIONS
OF MONGE-AMPERE EQUATIONS 109
CHAPTE
R 3
. GENERALIZE
D SOLUTION
S O
F IV-DIMENSIONA
L
MONGE-AMPER
E EQUATION
S 113
§5
. NORMAL MAPPING AND R-CURVATURE OF CONVEX FUNCTIONS 113
9.1
. SOME NOTATIO
N 113
9.2. NORMAL MAPPIN
G 113
9.3. CONVERGENCE LEMM
A OF SUPPORTIN
G HYPERPLANE
S 114
9.4. MAIN PROPERTIE
S OF TH
E NORMA
L MAPPIN
G
OF A CONVEX HYPERSURFAC
E 115
9.5. PROOFS 116
9.6. .R-CURVATURE OF CONVEX FUNETIONS 118
9.7. WEAK CONVERGENC
E OF IZ-CURVATURE
S 118
CONTENT
S XVII
§10. THE PROPERTIES OF CONVEX FUNCTIONS CONNECTED
URITH THEIR R-CURVATURE 123
10.1. THE COMPARISON AND UNIQUENESS THEOREMS 123
10.2. GEOMETRIE LEMMAS AND ESTIMATES 125
10.3. THE BORDER OF A CONVEX FUNCTION 127
10.4. CONVERGENCE OF CONVEX FUNCTIONS IN A CLOSED CONVEX DOMAIN.
COMPACTNESS THEOREMS 129
§11. GEOMETRIE THEORY OF THE MONGE-AMPERE EQUATIONS
AET{UIJ) = P(X)/R(DU) 146
11.1. INTRODUCTION. OBSTRUCTIONS AND NECESSARY CONDITIONS
OF SOLVABILITY FOR TH
E DIRICHLET PROBLEM 146
11.2. GENERALIZED AND WEAK SOLUTIONS FOR EQUATION (11.1) 148
11.3. THE DIRICHLET PROBLEM IN TH
E SET OF CONVEX FUNCTIONS
Q(A
U
A
2
,...,A
K
) 150
11.4. EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS
OF TH
E DIRICHLET PROBLEM FOR MONGE-AMPERE EQUATIONS
DET(UIJ) = P(X)/R(DU) 153
11.5. THE INVERSE OPERATOR FOR TH
E DIRICHLET PROBLEM 159
11.6. HYPERSURFACES WITH PRESCRIBED GAUSSIAN CURVATURE 161
§12. THE DIRICHLET PROBLEM FOR ELLIPTIC SOLUTIONS
OF MONGE-AMPERE EQUATIONS DET(UJJ) = F(X, U, DU) 166
12.1. THE FIRST MAIN EXISTENCE THEOREM
FOR TH
E DIRICHLET PROBLEM (12.1-2) 167
12.2. EXISTENCE OF A
T LEAST ONE GENERALIZED SOLUTION
OF TH
E DIRICHLET PROBLEM FOR EQUATIONS
DET(TIIJ) = F(X,U,DU) 170
12.3. EXISTENCE OF SEVERAL DIFFERENT GENERALIZED SOLUTIONS
FOR TH
E DIRICHLET PROBLEM (12.23-24) 173
CHAPTE
R 4
. VARIATIONA
L PROBLEM
S
AN
D GENERALIZE
D ELLIPTI
C SOLUTION
S
OF MONGE-AMPER
E EQUATION
S 182
§13. INTRODUCTION. THE MAIN PUNCTIONAL 182
13.1. STATEMENT OF PROBLEMS 182
13.2. PRELIMINARY CONSIDERATIONS 183
13.3. THE FUNCTIONAL IN (U) AND ITS PROPERTIES 184
§14. VARIATIONAL PROBLEM FOR THE FUNCTIONAL //
/ (U) 189
14.1. BILATERAL ESTIMATES FOR IH(U) 189
14.2. MAIN THEOREM ABOUT TH
E FUNCTIONAL J
# (U) 192
§15. DUAL CONVEX HYPERSURFACES AND EULER S EQUATION 193
15.1. SPECIAL MAP ON TH
E HEMISPHERE 194
15.2. DUAL CONVEX HYPERSURFACES 194
XVIII CONTENTS
15.3. EXPRESSION OF TH
E FUNCTIONAL IH (U) BY MEANS
OF DUAL CONVEX HYPERSURFACES 198
15.4. EXPRESSION OF TH
E VARIATION OF IH(U) 200
CHAPTER 5
. NON-COMPAC
T PROBLEM
S FOR ELLIPTI
C SOLUTION
S
OF MONGE-AMPER
E EQUATION
S 204
$16. INTRODUCTION. THE STATEMENT
OF THE SECOND BOUNDARY VALUE PROBLEM 204
16.1. ASYMPTOTIC CONE
OF INFINITE COMPLETE CONVEX HYPERSURFACES 204
16.2. TH
E STATEMENT OF TH
E SECOND BOUNDARY VALUE PROBLEM 205
$17. THE SECOND BOUNDARY VALUE PROBLEM
FOR MONGE-AMPERE EQUATIONS DET(UJJ) = NFOEL 207
17.1. THE NECESSARY AND SUFFICIENT CONDITIONS OF SOLVABILITY
OF TH
E SECOND BOUNDARY VALUE PROBLEM 207
17.2. TH
E SECOND BOUNDARY VALUE PROBLEM
IN TH
E CLASS OF CONVEX POLYHEDRA 208
$18. THE SECOND BOUNDARY VALUE PROBLEM
FOR GENERAL MONGE-AMPERE EQUATIONS 212
18.1. THE MAIN ASSUMPTIONS 212
18.2. TH
E STATEMENT OF TH
E MAIN THEOREM
AND TH
E SCHEME OF ITS PROOF. 213
18.3. THE FUNCTION SPACE
OF TH
E SECOND BOUNDARY VALUE PROBLEM 214
18.4. THE PROOF OF THEOREM 18.1 218
CHAPTE
R 6. SMOOT
H ELLIPTI
C SOLUTION
S
OF MONGE-AMPER
E EQUATION
S 226
$19. THE N-DIMENSIONAL MINKOWSKI PROBLEM 226
19.1. INTRODUCTION 226
19.2. A PRIORI ESTIMATES FOR TH
E RADII OF NORMAL CURVATURE
OF A CONVEX HYPERSURFACE 228
19.3. AUXILIARY CONCEPTS AND FORMULAS OBTAINED
BY E. CALABI [1] AND A. POGORELOV [3] 231
19.4. AN A PRIORI ESTIMATE FOR TH
E THIRD DERIVATIVES
OF A SUPPORT FUNCTION OF A CONVEX HYPERSURFACE 235
19.5. THE PROOF OF THEOREM 19.3 238
$20. THE DIRICHLET PROBLEM FOR SMOOTH ELLIPTIC SOLUTIONS
OF N-DIMENSIONAL MONGE-AMPERE EQUATIONS 241
20.1. THE UNIQUENESS AND COMPARISON THEOREMS 242
20.2. C-ESTIMATES FOR SOLUTIONS U{X) G C
2
(G)
OF TH
E DIRICHLET PROBLEM (20.2) BY SUBSOLUTIONS 244
20.3. GEOMETRIE ESTIMATES OF CONVEX SOLUTIONS
FOR MONGE-AMPERE EQUATIONS 252
CONTENT
S XIX
20.4
. GEOMETRI
E ESTIMATE
S OF TH
E GRADIEN
T OF CONVE
X SOLUTION
S
FOR MONGE-AMPER
E EQUATION
S 260
20.5
. TH
E DIRICHLE
T PROBLE
M
FOR TH
E MONGE-AMPER
E EQUATIO
N DET(UIJ) = IP(X) 264
20.6
. A PRIOR
I ESTIMATE
S FOR DERIVATIVE
S U
P T
O SECON
D ORDE
R 266
20.7
. CALABI
S INTERIO
R ESTIMATE
S FOR TH
E THIR
D DERIVATIVE
S 271
20.8
. ONE-SIDE
D ESTIMATE
S A
T TH
E BOUNDAR
Y
FOR SOM
E THIR
D DERIVATIVE
S 275
20.9
. A
N IMPORTAN
T LEMM
A 277
20.10. COMPLETIO
N OF TH
E PROO
F OF THEORE
M 20.8 280
20.11
. MOR
E GENERA
L MONGE-AMPER
E EQUATION
S 283
PAR
T III
. GEOMETRIE METHODS IN ELLIPTIC EQUATIONS
OF SECOND ORDER. APPLICATIONS T
O CALCULUS
OF VARIATIONS, DIFFERENTIAL GEOMETRY
AND APPLIED MATHEMATICS. 285
CHAPTE
R 7
. GEOMETRI
E CONCEPT
S AN
D METHOD
S
I
N NONLINEA
R ELLIPTI
C EULER-LAGRANG
E EQUATION
S 287
$21. GEOMETRIE CONSTRUCTIONS. TWO-SIDED C-ESTIMATES
OF FUNCTIONS WITH PRESCRIBED DIRICHLET DATA 288
21.1
. GEOMETRI
E CONSTRUCTION
S 288
21.2
. CONVE
X AN
D CONCAV
E SUPPORT
S
OF FUNCTION
S U{X) G W%(B) N C(B) .
^ ...
. 289
21.3
. TWO-SIDE
D C-ESTIMATE
S FOR FUNCTION
S U(X) E W(B) N C(B) ..
. 290
§22. APPLICATIONS TO THE DIRICHLET PROBLEM
FOR EULER-LAGRANGE EQUATIONS 297
§23. APPLICATIONS TO CALCULUS OF VARIATIONS, DIFFERENTIAL GEOMETRY
AND CONTINUUM MECHANICS 303
23.1
. APPLICATION
S T
O CALCULU
S OF VARIATION
S 303
23.2
. APPLICATION
S T
O DIFFERENTIAL GEOMETR
Y 306
23.3
. APPLICATION
S T
O CONTINUU
M MECHANIC
S 308
§24- C
2
-ESTIMATES FOR SOLUTIONS
OF GENERAL EULER-LAGRANGE ELLIPTIC EQUATIONS 312
24.1
. INTRODUCTIO
N 312
24.2
. MONGE-AMPER
E GENERATOR
S 313
24.3
. ASSUMPTION
S RELATE
D T
O GENERA
L EULER-LAGRANG
E EQUATION
S 323
24.4
. TWO-SIDE
D ESTIMATE
S FOR SOLUTION
S
OF NONLINEA
R ELLIPTI
C EULER-LAGRANG
E EQUATION
S 328
24.5
. TH
E SECOND TYP
E OF C-ESTIMATE
S FOR SOLUTION
S
FOR GENERA
L ELLIPTI
C EULER-LAGRANG
E EQUATION
S 330
CHAPTE
R 8
. TH
E GEOMETRI
E MAXIMU
M PRINCIPL
E
FO
R GENERA
L NON-DIVERGEN
T QUASILINEA
R ELLIPTI
C EQUATION
S 339
XX CONTENTS
$25. THE FIRST GEOMETRIE MAXIMUM PRINCIPLE FOR SOLUTIONS
OF THE DIRICHLET PROBLEM FOR GENERAL QUASILINEAR EQUATIONS 341
25.1. THE FIRST GEOMETRIE MAXIMUM PRINCIPLE
FOR GENERAL QUASILINEAR ELLIPTIC EQUATIONS
AND LINEAR ELLIPTIC EQUATIONS OF TH
E FORM 341
25.2. THE IMPROVEMENT OF ESTIMATES (25.16) FOR SOLUTIONS
OF GENERAL QUASILINEAR ELLIPTIC EQUATIONS DEPENDING
ON PROPERTIES OF TH
E FUNCTIONS
DET(AIFC(X,U,P)) AND B(X,U,P) 362
25.3. TH
E IMPROVEMENT OF ESTIMATE (25^106-107) AND (25.113)
FOR SOLUTIONS U{X) E W(B) N C{B) OF TH
E DIRICHLET PROBLEM
FOR EULER-LAGRANGE EQUATIONS 377
25.4. FINAL REMARKS RELATING T
O SUBSECTIONS 25.2 AND 25.3 380
25.5. POLAR RECIPROCAL CONVEX BODIES. ESTIMATES AND MAJORANTS
FOR SOLUTIONS OF TH
E DIRICHLET PROBLEMS (25.119-120)
AND (25.186-187) DEPENDING ON VOL(COOE
) 380
$26. THE GEOMETRIE MAXIMUM PRINCIPLE
FOR GENERAL QUASILINEAR ELLIPTIC EQUATIONS
(CONTINUATION AND DEVELOPMENT) 384
26.1. TH
E MAIN ASSUMPTIONS 385
26.2. CONCEPTS AND NOTATIONS RELATED T
O SOLUTIONS
OF TH
E DIRICHLET PROBLEM (26.1-2) 386
26.3. THE DEVELOPMENT OF TECHNIQUES RELATED
T
O FUNCTIONS Q
Q
(|P|) AND R( P ) 388
26.4. THE MAIN ESTIMATES FOR SOLUTIONS OF PROBLEM (26.1-2)
IF R(P) SATISFIES (26.9-A) 390
26.5. UNIFORM ESTIMATES FOR SOLUTIONS
OF TH
E DIRICHLET PROBLEM (26.1-2) (CONTINUATION
AND DEVELOPMENT OF SUBSECTION (26.4) 395
26.6. COMMENTS T
O TH
E MODIFIED CONDITION C.2 402
$27. POINTWISE ESTIMATES FOR SOLUTIONS OF THE DIRICHLET
PROBLEM FOR GENERAL QUASILINEAR ELLIPTIC EQUATIONS 405
27.1. INTEGRAL I(X,A,X
0
) 405
27.2. THE MAPPING S MEAN 407
27.3. THE GENERAL LEMMA OF CONVEXITY 409
27.4. THE POINTWISE ESTIMATES FOR SOLUTIONS
OF TH
E DIRICHLET PROBLEM (27.1-2) 413
$28. COMMENTS TO CHAPTER 8. THE MAXIMUM PRINCIPLES
IN GLOBAL PROBLEMS OF DIFFERENTIAL GEOMETRY 441
28.1. COMMENTS T
O CHAPTER 8 441
28.2. ESTIMATES FOR SOLUTIONS
OF QUASILINEAR ELLIPTIC EQUATIONS CONNECTED
WITH PROBLEMS OF GLOBAL GEOMETRY 442
CONTENT
S XXI
$29. THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS 446
29.1. INTRODUCTION 446
29.2. ESTIMATES FOR TH
E GRADIENT ON TH
E BOUNDARY
OF DB. (THE METHOD OF GLOBAL BARRIERS) 450
29.3. ESTIMATES OF TH
E GRADIENT
OF SOLUTIONS ON TH
E BOUNDARY.
(THE METHOD OF CONVEX MAJORANTS) 465
29.4. ESTIMATES OF TH
E GRADIENT OF SOLUTIONS ON TH
E BOUNDARY.
(THE METHOD OF SUPPORT HYPERPLANES) 473
29.5. GLOBAL GRADIENT ESTIMATES FOR SOLUTIONS
OF QUASILINEAR ELLIPTIC EQUATIONS 488
BIBLIOGRAPH
Y 497
INDE
X
509
|
| any_adam_object | 1 |
| author | Bakel'man, Il'ja Ja. 1928-1992 |
| author_GND | (DE-588)122949269 |
| author_facet | Bakel'man, Il'ja Ja. 1928-1992 |
| author_role | aut |
| author_sort | Bakel'man, Il'ja Ja. 1928-1992 |
| author_variant | i j b ij ijb |
| building | Verbundindex |
| bvnumber | BV009878684 |
| classification_rvk | SK 560 SK 620 |
| classification_tum | MAT 355f MAT 525f |
| ctrlnum | (OCoLC)243798553 (DE-599)BVBBV009878684 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009878684 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:42:30Z |
| institution | BVB |
| isbn | 3540136207 0387136207 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006543228 |
| oclc_num | 243798553 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-703 DE-739 DE-12 DE-824 DE-29T DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-703 DE-739 DE-12 DE-824 DE-29T DE-634 DE-83 DE-11 DE-188 |
| physical | XXI, 510 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| spelling | Bakel'man, Il'ja Ja. 1928-1992 Verfasser (DE-588)122949269 aut Convex analysis and nonlinear geometric elliptic equations Ilya J. Bakelman Berlin u.a. Springer 1994 XXI, 510 S. txt rdacontent n rdamedia nc rdacarrier Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s Konvexe Analysis (DE-588)4138566-4 s DE-604 Nichtlineare Differentialgleichung (DE-588)4205536-2 s Elliptische Differentialgleichung (DE-588)4014485-9 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006543228&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bakel'man, Il'ja Ja. 1928-1992 Convex analysis and nonlinear geometric elliptic equations Elliptische Differentialgleichung (DE-588)4014485-9 gnd Konvexe Analysis (DE-588)4138566-4 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4138566-4 (DE-588)4310554-3 (DE-588)4205536-2 |
| title | Convex analysis and nonlinear geometric elliptic equations |
| title_auth | Convex analysis and nonlinear geometric elliptic equations |
| title_exact_search | Convex analysis and nonlinear geometric elliptic equations |
| title_full | Convex analysis and nonlinear geometric elliptic equations Ilya J. Bakelman |
| title_fullStr | Convex analysis and nonlinear geometric elliptic equations Ilya J. Bakelman |
| title_full_unstemmed | Convex analysis and nonlinear geometric elliptic equations Ilya J. Bakelman |
| title_short | Convex analysis and nonlinear geometric elliptic equations |
| title_sort | convex analysis and nonlinear geometric elliptic equations |
| topic | Elliptische Differentialgleichung (DE-588)4014485-9 gnd Konvexe Analysis (DE-588)4138566-4 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Elliptische Differentialgleichung Konvexe Analysis Nichtlineare elliptische Differentialgleichung Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006543228&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bakelmaniljaja convexanalysisandnonlineargeometricellipticequations |