Sobolev gradients and differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Lecture notes in mathematics
1670 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 289 S. graph. Darst. |
| ISBN: | 9783642040405 |
Internformat
MARC
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| 245 | 1 | 0 | |a Sobolev gradients and differential equations |c J. W. Neuberger |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XIII, 289 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804140885417394176 |
|---|---|
| adam_text | CONTENTS 1 SEVERAL GRADIENTS 1 2 COMPARISON OF TWO GRADIENTS 5 2.1 A
GRAPHICAL COMPARISON BETWEEN TWO GRADIENTS 11 3 CONTINUOUS STEEPEST
DESCENT IN HUBERT SPACE: LINEAR CASE 15 4 CONTINUOUS STEEPEST DESCENT IN
HUBERT SPACE: NONLINEAR CASE 19 4.1 GLOBAL EXISTENCE 19 4.2 GRADIENT
INEQUALITY 21 4.3 WORK OF CHILL AND HUANG ON GRADIENT INEQUALITIES 30
4.4 HIGHER ORDER SOBOLEV SPACES FOR LOWER ORDER PROBLEMS 31 5 ORTHOGONAL
PROJECTIONS, ADJOINTS AND LAPLACIANS 35 5.1 A CONSTRUCTION OF A SOBOLEV
SPACE 35 5.2 A FORMULA OF VON NEUMANN 38 5.3 RELATIONSHIP BETWEEN
ADJOINTS 39 5.4 GENERAL LAPLACIANS 40 5.5 EXTENSION OF PROJECTIONS
BEYOND HUBERT SPACES 45 5.6 A GENERALIZED LAX-MILGRAM THEOREM 46 5.7
LAPLACIANS AND CLOSED LINEAR TRANSFORMATIONS 48 5.8 PROJECTIONS FOR
HIGHER ORDER SOBOLEV SPACES 51 6 ORDINARY DIFFERENTIAL EQUATIONS AND
SOBOLEV GRADIENTS 53 7 CONVEXITY AND GRADIENT INEQUALITIES 57
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/995796173 DIGITALISIERT
DURCH X CONTENTS 8 BOUNDARY AND SUPPLEMENTARY CONDITIONS 63 8.1
INTRODUCTION 63 8.2 ORTHOGONAL PROJECTION ONTO A NULL SPACE 65 8.3
PROJECTED SOBOLEV GRADIENTS, LINEAR CASE 65 8.4 PROJECTED GRADIENTS,
NONLINEAR CASE 66 8.5 EXPLICIT FORM FOR A PROJECTED GRADIENT 66 8.6
CONTINUOUS VS DISCRETE STEEPEST DESCENT 69 8.7 A FINITE DIMENSIONAL
EXAMPLE FOR ADJOINTS 70 8.8 APPROXIMATION OF PROJECTED GRADIENTS 73 8.9
AN EXAMPLE WITH MIXED BOUNDARY CONDITIONS 76 9 CONTINUOUS NEWTON S
METHOD 79 9.1 RIEMANNIAN METRICS AND A NASH-MOSER INVERSE FUNCTION
RESULT 79 9.2 NEWTON S METHOD FROM OPTIMIZATION 82 10 MORE ABOUT FINITE
DIFFERENCES 85 10.1 FINITE DIFFERENCES AND SOBOLEV GRADIENTS 85 10.2
SUPPLEMENTARY CONDITIONS AGAIN 88 10.3 GRAPHS AND SOBOLEV GRADIENTS 90
10.4 DIGRESSION ON ADJOINTS OF DIFFERENCE OPERATORS 92 10.5 A FIRST
ORDER PARTIAL DIFFERENTIAL EQUATION 92 10.6 A SECOND ORDER PARTIAL
DIFFERENTIAL EQUATION 95 11 SOBOLEV GRADIENTS FOR VARIATIONAL PROBLEMS
99 11.1 MINIMIZING SEQUENCES 99 11.2 EULER-LAGRANGE EQUATIONS 100 11.3
SOBOLEV GRADIENT APPROACH 100 12 AN INTRODUCTION TO SOBOLEV GRADIENTS IN
NON-INNER PRODUCT SPACES 103 13 SINGULARITIES AND A SIMPLE
GINZBURG-LANDAU FUNCTIONAL 10 CONTENTS XI 16 MINIMAL SURFACES 129 16.1
INTRODUCTION 129 16.2 MINIMUM CURVE LENGTH 129 16.3 MINIMAL SURFACES 132
16.4 UNIFORMLY PARAMETERIZED SURFACES 136 16.5 NUMERICAL METHODS AND
TEST RESULTS 140 16.6 CONCLUSION 145 17 FLOW PROBLEMS AND NON-INNER
PRODUCT SOBOLEV SPACES 147 17.1 FULL POTENTIAL EQUATION 147 17.2 OTHER
CODES FOR TRANSONIC FLOW 150 17.3 TRANSONIC FLOW PLOTS 151 18 AN
ALTERNATE APPROACH TO TIME-DEPENDENT PDES 153 18.1 INTRODUCTION 153 18.2
LEAST SQUARES METHOD 155 18.3 NUMERICAL RESULTS 156 19 FOLIATIONS AND
SUPPLEMENTARY CONDITIONS 1 159 19.1 A FOLIATION THEOREM 159 19.2 A
LINEAR EXAMPLE 168 20 FOLIATIONS AND SUPPLEMENTARY CONDITIONS II 171
20.1 SEMIGROUPS ON A METRIC SPACE 171 20.2 APPLICATION: SUPPLEMENTARY
CONDITION PROBLEM 172 20.3 COMPUTATIONAL FANTASY 174 21 SOME RELATED
ITERATIVE METHODS FOR DIFFERENTIAL EQUATIONS 177 22 AN ANALYTIC
ITERATION METHOD 187 23 STEEPEST DESCENT FOR CONSERVATION EQUATIONS 193
24 CODE FOR AN ORDINARY DIFFERENTIAL EQUATION 195 25 GEOMETRIC CURVE
MODELING WITH SOBOLEV GRADIENTS 199 25.1 INTRODUCTION 199 25. XII
CONTENTS 26 NUMERICAL DIFFERENTIATION, SOBOLEV GRADIENTS 209 26.1
INTRODUCTION 209 26.2 THE FUNCTIONAL H(Q) 212 26.3 STABILITY 216 26.4
STEEPEST DESCENT MINIMIZATION 217 26.5 SOME NUMERICAL EXAMPLES 219 26.6
RELATED INVERSE PROBLEMS 221 27 STEEPEST DESCENT AND NEWTON S METHOD AND
ELLIPTIC PDE 225 27.1 INTRODUCTION 225 27.2 THE VARIATIONAL FORMULATION
FOR PDE AND PDE 226 27.3 ALGORITHMS 230 27.3.1 THE *** AND MMPA 231
27.3.2 THEGNGA 232 27.3.3 TANGENT-AUGMENTED NEWTON S METHOD (TGNGA) ...
233 27.3.4 THE SECANT METHOD 233 27.3.5 CYLINDER-AUGMENTED NEWTON S
METHOD (CGNGA)... 234 27.4 SOME PDE AND PDE RESULTS 235 28
GINZBURG-LANDAU SEPARATION PROBLEMS 239 28.1 INTRODUCTION 239 28.2 MODEL
A 240 28.3 WEIGHTED GRADIENTS 241 28.4 MODEL A 241 28.5 A PHASE
SEPARATION PROBLEM 242 28.6 AN ELASTICITY PROBLEM 243 29 NUMERICAL
PRECONDITIONING METHODS FOR ELLIPTIC PDES 245 29.1 INTRODUCTION 245 29.2
THE MODEL PROBLEM 246 29.3 CONDITION NUMBERS OF NONLINEAR OPERATORS 247
29.4 FIXED PRECONDITIONED: SOBOLEV GRADIENTS WITH FIXED INNER PRODUCT
248 29.4.1 SOBOLEV GRADIENTS AND LAPLACIAN PRECONDITIONERS ... 249
29.4.2 GENERAL PRECONDITIONERS AS WEIGHTED SOBOLE CONTENTS XIII 30 MORE
RESULTS ON SOBOLEV GRADIENT PROBLEMS 259 30.1 SINGULAR BOUNDARY VALUE
PROBLEMS 259 30.2 QUANTUM MECHANICAL CALCULATIONS 260 30.3 DUAL STEEPEST
DESCENT 261 30.4 OPTIMAL EMBEDDING CONSTANTS FOR SOBOLEV SPACES 262 30.5
PERFORMANCE OF PRECONDITIONERS AND **_ I METHODS 262 30.6
POISSON-BOLTZMANN EQUATION 263 30.7 TIME INDEPENDENT NAVIER-STOKES 263
30.8 STEEPEST DESCENT AND HYPERBOLIC MONGE-AMPERE EQUATIONS 264 30.9
APPLICATION TO DIFFERENTIAL ALGEBRAIC EQUATIONS 265 30.10 CONTROL THEORY
AND PDE 266 30.11 AN ELASTICITY PROBLEM 267 30.12 A LIQUID CRYSTAL
PROBLEM 267 30.13 APPLICATIONS TO FUNCTIONAL DIFFERENTIAL EQUATIONS 268
30.14 MORE ABOUT ACTIVE CONTOURS 269 30.15 ANOTHER SOLUTION GIVING
NONLINEAR PROJECTION 270 30.16 DYNAMICS OF STEEPEST DESCENT 271 30.17
AUBRY-MATHER THEORY AND A COMPARISON PRINCIPLE FOR A SOBOLEV GRADIENT
DESCENT 271 31 NOTES AND SUGGESTIONS FOR FUTURE WORK 273 REFERENCES 277
INDEX 287
|
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| author | Neuberger, John W. 1934- |
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| author_facet | Neuberger, John W. 1934- |
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| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T22:07:05Z |
| institution | BVB |
| isbn | 9783642040405 |
| language | English |
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| physical | XIII, 289 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Neuberger, John W. 1934- Verfasser (DE-588)115580158 aut Sobolev gradients and differential equations J. W. Neuberger 2. ed. Berlin [u.a.] Springer 2010 XIII, 289 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1670 Gradientenverfahren (DE-588)4157995-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Gradientenverfahren (DE-588)4157995-1 s DE-604 Lecture notes in mathematics 1670 (DE-604)BV000676446 1670 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018762108&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neuberger, John W. 1934- Sobolev gradients and differential equations Lecture notes in mathematics Gradientenverfahren (DE-588)4157995-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4157995-1 (DE-588)4044779-0 |
| title | Sobolev gradients and differential equations |
| title_auth | Sobolev gradients and differential equations |
| title_exact_search | Sobolev gradients and differential equations |
| title_full | Sobolev gradients and differential equations J. W. Neuberger |
| title_fullStr | Sobolev gradients and differential equations J. W. Neuberger |
| title_full_unstemmed | Sobolev gradients and differential equations J. W. Neuberger |
| title_short | Sobolev gradients and differential equations |
| title_sort | sobolev gradients and differential equations |
| topic | Gradientenverfahren (DE-588)4157995-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Gradientenverfahren Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018762108&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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