Topics on concentration phenomena and problems with multiple scales:
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York
Springer
2006
|
| Schriftenreihe: | Lecture notes of the Unione Matematica Italiana
2 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-540-36546-4 https://doi.org/10.1007/978-3-540-36546-4 https://doi.org/10.1007/978-3-540-36546-4 https://doi.org/10.1007/978-3-540-36546-4 https://doi.org/10.1007/978-3-540-36546-4 https://doi.org/10.1007/978-3-540-36546-4 https://doi.org/10.1007/978-3-540-36546-4 https://doi.org/10.1007/978-3-540-36546-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015586451&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturangaben |
| Umfang: | 1 Online-Ressource (X, 316 S.) graph. Darst. |
| ISBN: | 354036241X 9783540362418 9783540365464 |
| DOI: | 10.1007/978-3-540-36546-4 |
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Datensatz im Suchindex
| DE-BY-TUM_katkey | 1963243 |
|---|---|
| _version_ | 1821930762615652352 |
| adam_text | ANDREA BRAIDES YY VALERIA CHIADO PIAT (EDS.)
TOPICS
ON CONCENTRATION
PHENOMENA AND PROBLEMS
WITH MULTIPLE SCALES
FYJ
SPRINGE
R
UMI
CONTENTS
PART I PROBLEM
S WIT
H MULTIPL
E SCALE
S
FROM DISCRET
E SYSTEM
S T
O CONTINUOU
S VARIATIONAL PROBLEMS
: AN
INTRODUCTIO
N
ANDREA BRAIDES AND MARIA STELLA GELLI
3
1 DISCRET
E PROBLEM
S WIT
H LIMI
T ENERGIES DEFINED O
N SOBOLEV SPACE
S ...
. 6
1.1 DISCRET
E MNCTIONAL
S 6
1.2 EQUIVALEN
T ENERGIES O
N SOBOLEV FUNCTIONS 7
1.3 CONVEX ENERGIES 8
1.4 NON-CONVEX ENERGIES WIT
H SUPE
R LINEA
R GROWT
H 11
1.5 A GENERA
L CONVERGENCE THEORE
M 19
1.6 CONVERGENCE OF MINIMU
M PROBLEM
S 21
1.7 MOR
E EXAMPLE
S 28
1.8 ENERGIE
S DEPENDIN
G O
N SECOND-DIFFERENCE QUOTIENT
S 35
2 LIMI
T ENERGIES O
N DISCONTINUOU
S FUNCTIONS: TWO EXAMPLE
S 36
2.1 TH
E BLAKE-ZISSERMA
N MODE
L 36
2.2 SECOND-DIFFERENCE INTERACTION
S 51
2.3 LENNARD-JONE
S POTENTIAL
S 52
2.4 RENORMALIZATION-GROU
P APPROAC
H 58
3 GENERA
L CONVERGENCE RESULT
S 58
3.1 FUNCTION
S OF BOUNDE
D VARIATIO
N 58
3.2 NEAREST-NEIGHBOU
R INTERACTION
S 60
3.3 LONG-RANG
E INTERACTION
S 73
REFERENCES 75
RELAXATIO
N FOR BULK AND INTERFACIAL ENERGIE
S
ANNELIESE DEFRANCESCHI
79
1 INTRODUCTIO
N 79
2 LOWER SEMICONTINUIT
Y - TH
E DIREC
T METHO
D OF TH
E CALCULU
S OF
VARIATION
S 81
3 RELAXATIO
N 83
VIII CONTENTS
4 PRELIMINARIES. FUNCTIONS OF BOUNDED VARIATION AND SPECIAL FUNCTIONS
OF BOUNDED VARIATION 85
4.1 NOTATION 85
4.2 MEASURE SPACES 86
4.3 FUNCTIONS OF BOUNDED VARIATION 88
4.4 SETS OF FINITE PERIMETER 90
4.5 STRUCTURE OF
BV
FUNCTIONS. APPROXIMATE DISCONTINUITY POINTS
AND APPROXIMATE JUMP POINTS 91
4.6 SPECIAL FUNCTIONS OF BOUNDED VARIATION 92
4.7
BV (SBV)
FUNCTIONS IN ONE DIMENSION 92
5 LOWER SEMICONTINUITY AND RELAXATION IN ONE DIMENSION 93
5.1 A CHARACTERIZATION OF L.S.C. FOR FUNCTIONALS DEFINED ON
SBV (I).
RELAXATION ON
BV(I)
93
5.2 A SUFFICIENT CONDITION FOR L.S.C. FOR FUNCTIONALS DEFINED ON
SBV (I).
RELAXATION IN
BV(I)
100
6 LOWER SEMICONTINUITY AND RELAXATION IN HIGHER DIMENSION 106
7 LOWER SEMICONTINUITY AND RELAXATION IN HIGHER DIMENSION AND FOR
VECTOR-VALUED FUNCTIONS 113
7.1 UPPER BOUND FOR TH
E RELAXED FUNCTIONAL 119
7.2 DE GIORGI-LETTA CRITERION T
O PROVE MEASURE PROPERTIES OF THE
RELAXED FUNCTIONAL 121
7.3 INTEGRAL REPRESENTATION 125
7.4 PROOF OF THE MAIN THEOREM 126
8 RELAXATION IN HIGHER DIMENSION (ISOTROPY ASSUMPTIONS) 129
9 APPENDIX 132
9.1 APPENDIX A: LOWER SEMICONTINUOUS ENVELOPE 132
9.2 APPENDIX B: PROOF OF (73) 135
9.3 APPENDIX C: PROOF OF STEP 3 IN PROPOSITION 67 135
REFERENCES 136
CONVERGENCE OF DIRICHLE
T FORMS O
N FRACTALS
ROBERTO PEIRONE
139
1 INTRODUCTION 139
2 CONSTRUCTION OF AN ENERGY ON TH
E GASKET 141
3 DIRICHLET FORMS ON FINITELY RAMIFIED FRACTALS 152
4 MAIN PROPERTIES OF RENORMALIZATION AND HARMONIC EXTENSION 164
5 HOMOGENIZATION ON THE GASKET 173
6 HOMOGENIZATION ON GENERAL FRACTALS 179
REFERENCES 188
HOMOGENIZATIO
N IN PERFORATE
D DOMAIN
S
GREGORY A. CHECHKIN
189
1 APPEARENCE OF A TERM ETRANGE . DIRICHLET PROBLEMS IN DOMAINS
WITH LOW CONCENTRATION OF HOLES 190
1.1 BASIC NOTATION^AND SETTING OF TH
E PROBLEM 190
CONTENTS IX
1.2 THE HOMOGENIZATION THEOREM 191
2 HOMOGENIZATION PROBLEMS IN PERFORATED DOMAIN WITH OSCILLATING
FOURIER BOUNDARY CONDITIONS 193
2.1 BASIC NOTATION 193
2.2 FORMAL ASYMPTOTIC ANALYSIS OF THE PROBLEM .
. 194
2.3 MAIN ESTIMATES AND RESULTS 197
2.4 AUXILIARY RESULTS 199
2.5 JUSTIFICATION OF ASYMPTOTICS 203
REFERENCES 207
HOMOGENIZATIO
N OF RANDO
M NO
N STATIONAR
Y PARABOLIC OPERATOR
S
ANDREY PIATNITSKI
209
1 THE SETUP 210
2 FACTORIZATION OF THE EQUATION 213
3 A PRIORI ESTIMATES FOR THE FACTORIZED EQUATION 214
4 AUXILIARY PROBLEMS 215
5 HOMOGENIZATION OF THE FACTORIZED EQUATION 218
6 HOMOGENIZATION OF THE ORIGINAL EQUATION 223
7 EQUATIONS WITH DIFFUSION DRIVING PROCESS 225
REFERENCES 230
PART II PROBLEM
S WIT
H CONCENTRATIO
N
^-CONVERGENC
E FOR CONCENTRATIO
N PROBLEM
S
ADRIANA GARRONI
233
1 INTRODUCTION 233
2 TWO CLASSICAL EXAMPLES 234
2.1 SOBOLEV INEQUALITY 235
2.2 CAPACITY AND ISOPERIMETRIC INEQUALITY FOR TH
E CAPACITY 238
3 THE GENERAL PROBLEM 242
3.1 VARIATIONAL FORMULATION 242
3.2 GENERALIZED SOBOLEV INEQUALITY 244
3.3 CONCENTRATION 244
3.4 /^-CONVERGENCE 245
3.5 THE CONCENTRATION RESULT IN TERMS OF /^-CONVERGENCE 246
4 IDENTIFICATION OF THE CONCENTRATION POINT 252
4.1 THE GREEN S FUNCTION AND THE ROBIN FUNCTION 253
4.2 ASYMPTOTIC EXPANSION IN /^-CONVERGENCE 256
4.3 THE RESULT 257
4.4 HARMONIC TRANSPLANTATION 260
5 IRREGULAR DOMAINS 263
REFERENCES 265
X CONTENTS
GAMMA-CONVERGENCE OF GRADIENT FLOWS AND APPLICATION
S T
O
GINZBURG-LANDAU VORTE
X DYNAMIC
S
SYLVIA SERFATY
267
1 INTRODUCTION 267
1.1 PRESENTATION OF THE GINZBURG-LANDAU MODEL 267
1.2 GAMMA-CONVERGENCE 269
1.3 / -CONVERGENCE OF GINZBURG-LANDAU 271
2 THE ABSTRACT RESULT FOR JT-CONVERGENCE OF GRADIENT-FLOWS 275
2.1 THE ABSTRACT SITUATION 275
2.2 THE RESULT 276
2.3 INTERPRETATION 279
2.4 IDEA OF THE PROOF 279
2.5 APPLICATION TO GINZBURG-LANDAU 281
2.6 REMARKS 282
3 PROOF OF THE ADDITIONAL CONDITIONS FOR GINZBURG-LANDAU 284
3.1 A PRODUCT-ESTIMATE FOR GINZBURG-LANDAU 284
3.2 IDEA OF THE PROOF 285
3.3 APPLICATION T
O THE DYNAMICS 286
3.4 PROOF OF THE CONSTRUCTION 2 ) 287
4 EXTENSIONS OF THE METHOD 289
4.1 COLLISIONS 289
4.2 SECOND ORDER QUESTIONS - STABILITY ISSUES 290
REFERENCES 291
PD
E ANALYSIS OF CONCENTRATIN
G ENERGIE
S FOR TH
E GINZBURG
LANDAU EQUATIO
N
DIDIER SMETS
293
1 INTRODUCTION 293
2 THE MONOTONICITY FORMULA 294
2.1 SCALING PROPERTIES 294
2.2 THE MONOTONICITY FORMULA 295
2.3 CONSEQUENCES FOR /X* 297
3 REGULARITY THEOREMS FOR (GL)
E
299
3.1 BOCHNER, SMALL ENERGY REGULARITY AND CLEARING-OUT 299
3.2 CONSEQUENCES FOR /Z* 306
4 POTENTIAL AND MODULUS ESTIMATES 308
5
E^
IS A MINIMAL SURFACE 311
5.1 CLASSICAL AND WEAK NOTIONS OF MEAN CURVATURE 311
5.2 DERIVING THE CURVATURE EQUATION 312
REFERENCES 314
INDEX 315
|
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| dewey-full | 515.64 |
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| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-3-540-36546-4 |
| format | Electronic eBook |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV022377403 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:54:04Z |
| institution | BVB |
| isbn | 354036241X 9783540362418 9783540365464 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015586451 |
| oclc_num | 315824884 |
| open_access_boolean | |
| owner | DE-739 DE-355 DE-BY-UBR DE-634 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-739 DE-355 DE-BY-UBR DE-634 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 DE-19 DE-BY-UBM |
| physical | 1 Online-Ressource (X, 316 S.) graph. Darst. |
| psigel | ZDB-2-SMA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes of the Unione Matematica Italiana |
| series2 | Lecture notes of the Unione Matematica Italiana |
| spellingShingle | Topics on concentration phenomena and problems with multiple scales Lecture notes of the Unione Matematica Italiana Homogenisierungsmethode (DE-588)4257770-6 gnd Variationsproblem (DE-588)4187419-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4257770-6 (DE-588)4187419-5 (DE-588)4126634-1 (DE-588)4143413-4 |
| title | Topics on concentration phenomena and problems with multiple scales |
| title_auth | Topics on concentration phenomena and problems with multiple scales |
| title_exact_search | Topics on concentration phenomena and problems with multiple scales |
| title_full | Topics on concentration phenomena and problems with multiple scales Andrea Braides ; Valeria Chiadò Piat (ed.) |
| title_fullStr | Topics on concentration phenomena and problems with multiple scales Andrea Braides ; Valeria Chiadò Piat (ed.) |
| title_full_unstemmed | Topics on concentration phenomena and problems with multiple scales Andrea Braides ; Valeria Chiadò Piat (ed.) |
| title_short | Topics on concentration phenomena and problems with multiple scales |
| title_sort | topics on concentration phenomena and problems with multiple scales |
| topic | Homogenisierungsmethode (DE-588)4257770-6 gnd Variationsproblem (DE-588)4187419-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Homogenisierungsmethode Variationsproblem Asymptotik Aufsatzsammlung |
| url | https://doi.org/10.1007/978-3-540-36546-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015586451&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035421262 |
| work_keys_str_mv | AT braidesandrea topicsonconcentrationphenomenaandproblemswithmultiplescales |