Variational and quasivariational inequalities: applications to free boundary problems
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Italian |
| Published: |
Chichester ; New York ; Brisbane ; Toronto ; Singapore
Wiley
1984
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Disequazioni variazionali e quasivariazionali <engl.>. - Aus d. Ital. übers. |
| Physical Description: | IX, 452 Seiten Diagramme |
| ISBN: | 0471902012 |
Staff View
MARC
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| 100 | 1 | |a Baiocchi, Claudio |d 1940-2020 |0 (DE-588)1167817907 |4 aut | |
| 240 | 1 | 0 | |a Disequazioni variazionali e quasivariazionali |
| 245 | 1 | 0 | |a Variational and quasivariational inequalities |b applications to free boundary problems |c Claudio Baiocchi and António Capelo |
| 264 | 1 | |a Chichester ; New York ; Brisbane ; Toronto ; Singapore |b Wiley |c 1984 | |
| 300 | |a IX, 452 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a EST: Disequazioni variazionali e quasivariazionali <engl.>. - Aus d. Ital. übers. | ||
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Variational inequalities (Mathematics) | |
| 700 | 1 | |a Capelo, Antonio |0 (DE-588)1167818393 |4 aut | |
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Record in the Search Index
| _version_ | 1804114752854556672 |
|---|---|
| adam_text | CONTENTS
PREFACE........................
IX
PART
I
VARIATIONAL
PROBLEMS
CHAPTER
1
INTRODUCTION....................
3
1.1
EXAMPLE
OF
A
VARIATIONAL
PROBLEM.
THE
NOTION
OF
WELL-
POSED
PROBLEM.....................
3
1.2
SOME
EXISTENCE
RESULTS
.................
6
CHAPTER
2
MINIMIZATION
OF
CONVEX
FUNCTIONALS
.........
9
2.1
FUNDAMENTAL
THEOREM
.................
9
2.2
VARIATIONAL
FORMULATION
OF
A
MINIMIZATION
PROBLEM.....
15
2.3
PROJECTIONS
ON
CONVEX
SETS................
18
CHAPTER
3
VARIATIONAL
INEQUALITIES...............
21
3.1
FUNDAMENTAL
THEOREM
.................
21
3.2
MINIMIZATION
OF
CONVEX
FUNCTIONALS............
30
3.2.1
GATEAUX
DERIVATIVE.................
30
3.2.2
GENERAL
RESULTS...................
34
3.2.3
THE
CONCEPT
OF
SUBDIFFERENTIAL............
37
CHAPTER
4
TRANSPOSITION
OF
OPERATORS.
APPLICATIONS
.......
41
4.1
THE
CONCEPT
OF
TRANSPOSITION.
FUNDAMENTAL
PROPERTIES
....
41
4.2
APPLICATIONS
OF
THE
CONCEPT
OF
TRANSPOSITION........
45
4.2.1
SOME
EXAMPLES
OF
FUNCTION
SPACES
IMPORTANT
IN
THE
APPLI
CATIONS.
EXAMPLES
OF
CONTINUOUS
LINEAR
OPERATORS
....
47
4.2.2
DUAL
SPACES
AND
TRANSPOSED
OPERATORS.........
55
CHAPTER
5
SOBOLEV
SPACES
..................
67
5.1
ON
THE
NECESSITY
FOR
NEW
FUNCTION
SPACES
.........
67
5.2
SPACES
W
S
-
P
(IR
N
)
....................
69
5.3
SPACES
W^FT).....................
84
5.4
SPACES
W
!
-
P
(T).....................
93
5.5
NORMAL
CONTRACTIONS
AND
DIRICHLET
SPACES
.........
99
V
VI
CHAPTER
6
EXAMPLES
OF
VARIATIONAL
PROBLEMS
IN
ONE
DIMENSION
.
.
104
6.1
THE
OBSTACLE
PROBLEM.
GENERALITIES
ABOUT
REGULARITY
RESULTS
.
104
6.2
SOME
CONSIDERATIONS
REGARDING
SECOND
ORDER
LINEAR
PROBLEMS
.
112
CHAPTER
7
EXAMPLES
OF
VARIATIONAL
PROBLEMS
IN
SEVERAL
DIMEN
SIONS
.......................119
7.1
GENERAL
COMMENTS
ON
DIFFERENTIAL
OPERATORS........119
7.2
LINEAR
PROBLEMS....................129
7.2.1
INTRODUCTION.
THE
HOMOGENEOUS
DIRICHLET
PROBLEM
.
.
.
129
7.2.2
GENERAL
FORMULATION
IN
VARIATIONAL
TERMS........137
7.2.3
EXAMPLES
OF
BOUNDARY
VALUE
PROBLEMS
........143
7.3
NONLINEAR
PROBLEMS
..................156
7.4
REGULARITY
RESULTS
...................169
7.4.1
REGULARITY
OF
THE
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
...
169
7.4.2
REGULARITY
OF
SOLUTIONS
OF
VARIATIONAL
INEQUALITIES
....
174
CHAPTER
8
VARIATIONAL
FORMULATION
OF
A
FREE-BOUNDARY
PROBLEM
.
183
8.1
GENERALITIES.
THE
PHYSICAL
PROBLEM............183
8.2
TRANSFORMATION
OF
THE
PROBLEM..............187
8.3
QUASIVARIATIONAL
PROBLEMS................190
PART
II
QUASIVARIATIONAL
PROBLEMS
CHAPTER
9
FIXED
POINT
THEOREMS
...............199
9.1
INTRODUCTION......................199
9.2
FIXED
POINT
THEOREMS
FOR
LIPSCHITZ
CONTINUOUS
APPLICATIONS
.
201
9.2.1
SINGLE-VALUED
APPLICATIONS:
BANACH
THEOREM......201
9.2.2
MULTI-VALUED
APPLICATIONS
..............204
9.3
FIXED
POINT
THEOREMS
FOR
CONTINUOUS
APPLICATIONS......205
9.3.1
THE
KNASTER-KURATOWSKI-MAZURKIEWICZ
LEMMA
AND
THE
FAN
LEMMA
....................205
9.3.2
SINGLE-VALUED
APPLICATIONS:
THE
THEOREMS
OF
BROUWER,
SCHAUDER
AND
TYCHONOV...............210
9.3.3
MULTI-VALUED
APPLICATIONS
..............216
9.4
FIXED
POINT
THEOREMS
FOR
MONOTONE
APPLICATIONS
......222
CHAPTER
10
SOME
RESULTS
ON
THE
EXISTENCE
OF
SOLUTIONS
OF
VARIA
TIONAL
INEQUALITIES.................226
10.1
GENERAL
RESULTS
OF
EXISTENCE
..............226
10.2
PARTICULAR
CASES.
I...................232
10.3
PARTICULAR
CASES.
II
..................234
CHAPTER
11
QUASIVARIATIONAL
INEQUALITIES............237
11.1
INTRODUCTION
.....................237
VLL
11.2
TECHNIQUES
OF
MONOTONICITY
..............244
11.3
TECHNIQUES
OF
COMPACTNESS...............253
CHAPTER
12
FREE-BOUNDARY
PROBLEMS
.............262
12.1
INTRODUCTION
.....................262
12.2
THE
PHYSICAL
PROBLEM
.................264
12.3
THE
MATHEMATICAL
PROBLEM...............276
12.3.1
RIGOROUS
FORMULATION
OF
THE
FREE-BOUNDARY
PROBLEM
.
.
277
12.3.2
TRANSFORMATION
OF
THE
FREE-BOUNDARY
PROBLEM.....280
12.3.3
STUDY
OF
A
LINEAR
MIXED
PROBLEM...........286
12.3.4
STUDY
OF
A
NONLINEAR
MIXED
PROBLEM.........291
12.3.5
STUDY
OF
A
QUASIVARIATIONAL
PROBLEM.
EXISTENCE
OF
THE
SOLUTION
OF
A
FREE-BOUNDARY
PROBLEM.........294
12.3.6
UNIQUENESS
AND
REGULARITY
OF
THE
SOLUTION
OF
A
FREE
BOUNDARY
PROBLEM.................302
12.3.7
DAM
WITH
VERTICAL
WALLS
..............304
CHAPTER
13
FREE-BOUNDARY
PROBLEMS
AND
VARIATIONAL
INEQUALITIES
.
317
PART
III
TECHNICAL
TOOLS
CHAPTER
14
SEMINORMS....................325
CHAPTER
15
REGULARIZATION
AND
PARTITION
OF
THE
UNIT.......335
15.1
REGULARIZATION
....................335
15.2
PARTITION
OF
THE
UNIT..................342
CHAPTER
16
ON
THE
REGULARITY
OF
THE
OPEN
SETS.........346
16.1
MANIFOLDS.
OPEN
SETS
OF
CLASS
C
K
AND
C
K,M
.
CONE
AND
SEGMENT
PROPERTIES
......................346
16.2
DISTRIBUTIONS
ON
A
MANIFOLD.
SPACES
L
P
(T)
........353
CHAPTER
17
THE
MAXIMUM
PRINCIPLE
AND
ITS
APPLICATIONS.....357
17.1
INTRODUCTION
.....................357
17.2
MAXIMUM
PRINCIPLE
IN
1R................357
17.3
MAXIMUM
PRINCIPLE
IN
C................361
17.4
MAXIMUM
PRINCIPLE
IN
R ................365
17.5
COMPLEMENTS.....................368
CHAPTER
18
ON
GREEN*S
FORMULAE...............370
CHAPTER
19
ORDERED
STRUCTURES
................381
19.1
BASIC
DEFINITIONS
...................381
19.2
LATTICES
.......................384
19.3
ORDERED
VECTOR
SPACES.
VECTOR
LATTICES..........388
VLIL
19.4
TOPOLOGICAL
VECTOR
LATTICES.
BANACH-RIESZ
SPACES
.....393
19.5
HILBERT
PSEUDO-LATTICES.................399
CHAPTER
20
MULTI-VALUED
MAPPINGS
..............401
20.0
NOTATIONS
......................401
20.1
FUNDAMENTAL
DEFINITIONS................401
20.2
TOPOLOGIES
IN
2I
...................405
20.2.1
THE
HAUSDORFF
METRIC
TOPOLOGY
...........405
20.2.2
VIETORIS
TOPOLOGIES
................408
20.3
ORDERS
IN
2.....................414
BIBLIOGRAPHY.........................417
INDEX
............................449
SPECIAL
FUNCTION
SPACES
INDEX..................452
|
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| id | DE-604.BV000288275 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:11:43Z |
| institution | BVB |
| isbn | 0471902012 |
| language | English Italian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000175321 |
| oclc_num | 9533468 |
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| physical | IX, 452 Seiten Diagramme |
| psigel | TUB-nveb |
| publishDate | 1984 |
| publishDateSearch | 1984 |
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| publisher | Wiley |
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| spelling | Baiocchi, Claudio 1940-2020 (DE-588)1167817907 aut Disequazioni variazionali e quasivariazionali Variational and quasivariational inequalities applications to free boundary problems Claudio Baiocchi and António Capelo Chichester ; New York ; Brisbane ; Toronto ; Singapore Wiley 1984 IX, 452 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier EST: Disequazioni variazionali e quasivariazionali <engl.>. - Aus d. Ital. übers. Boundary value problems Variational inequalities (Mathematics) Capelo, Antonio (DE-588)1167818393 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000175321&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baiocchi, Claudio 1940-2020 Capelo, Antonio Variational and quasivariational inequalities applications to free boundary problems Boundary value problems Variational inequalities (Mathematics) |
| title | Variational and quasivariational inequalities applications to free boundary problems |
| title_alt | Disequazioni variazionali e quasivariazionali |
| title_auth | Variational and quasivariational inequalities applications to free boundary problems |
| title_exact_search | Variational and quasivariational inequalities applications to free boundary problems |
| title_full | Variational and quasivariational inequalities applications to free boundary problems Claudio Baiocchi and António Capelo |
| title_fullStr | Variational and quasivariational inequalities applications to free boundary problems Claudio Baiocchi and António Capelo |
| title_full_unstemmed | Variational and quasivariational inequalities applications to free boundary problems Claudio Baiocchi and António Capelo |
| title_short | Variational and quasivariational inequalities |
| title_sort | variational and quasivariational inequalities applications to free boundary problems |
| title_sub | applications to free boundary problems |
| topic | Boundary value problems Variational inequalities (Mathematics) |
| topic_facet | Boundary value problems Variational inequalities (Mathematics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000175321&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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