Parabolic quasilinear equations minimizing linear growth functionals:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel
Birkhäuser
2004
|
| Series: | Progress in mathematics
223 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 340 S. Ill. |
| ISBN: | 9783764366193 3764366192 0817666192 |
Staff View
MARC
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| 100 | 1 | |a Andreu-Vaillo, Fuensanta |d 1955-2008 |e Verfasser |0 (DE-588)135629896 |4 aut | |
| 245 | 1 | 0 | |a Parabolic quasilinear equations minimizing linear growth functionals |c Fuensanta Andreu-Vaillo ; Vicent Caselles ; José M. Mazón |
| 264 | 1 | |a Basel |b Birkhäuser |c 2004 | |
| 300 | |a XIV, 340 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 223 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Différences finies | |
| 650 | 7 | |a Equações diferenciais parciais parabólicas |2 larpcal | |
| 650 | 4 | |a Opérateurs non linéaires | |
| 650 | 4 | |a Traitement d'images - Mathématiques | |
| 650 | 4 | |a Équations différentielles non linéaires | |
| 650 | 4 | |a Équations différentielles paraboliques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Differential equations, Parabolic | |
| 650 | 4 | |a Finite differences | |
| 650 | 4 | |a Image processing |x Mathematics | |
| 650 | 4 | |a Nonlinear operators | |
| 650 | 0 | 7 | |a Parabolische Differentialgleichung |0 (DE-588)4173245-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 Total Variation Based Image Restoration 1
1.1 Introduction 1
1.2 Equivalence between Constrained and Unconstrained Restoration . 8
1.3 The Partial Differential Equation Satisfied by the Minimum of (1.17) 13
1.4 Algorithm and Numerical Experiments 18
1.5 Review of Numerical Methods 25
2 The Neumann Problem for the Total Variation Flow 31
2.1 Introduction 31
2.2 Strong Solutions in L2(fi) 33
2.3 The Semigroup Solution in L^fi) 35
2.4 Existence and Uniqueness of Weak Solutions 42
2.5 An LN L°° Regularizing Effect 47
2.6 Asymptotic Behaviour of Solutions 50
2.7 Regularity of the Level Lines 55
3 The Total Variation Flow in RN 57
3.1 Initial Conditions in L2(RN) 57
3.2 The Notion of Entropy Solution 62
3.3 Uniqueness in Lloc(RN) 63
3.4 Existence in L^R^) 69
3.5 Initial Conditions in L^R^) 71
3.6 Time Regularity 72
3.7 An LN L°° Regularizing Effect 77
3.8 Measure Initial Conditions 77
4 Asymptotic Behaviour and Qualitative Properties of Solutions 81
4.1 Radially Symmetric Explicit Solutions 81
4.2 Some Qualitative Properties 87
4.3 Asymptotic Behaviour 92
viii Contents
4.4 Evolution of Sets in R2: The Connected Case 103
4.5 Evolution of Sets in IR2: The Nonconnected Case 114
4.6 Some Examples 118
4.7 Explicit Solutions for the Denoising Problem 120
5 The Dirichlet Problem for the Total Variation Flow 125
5.1 Introduction 125
5.2 Definitions and Preliminary Facts 126
5.3 The Main Result 129
5.4 The Semigroup Solution 129
5.5 Strong Solutions for Data in L2(Q) 143
5.6 Existence and Uniqueness for Data in L1^) 148
5.7 Regularity for Positive Initial Data 159
6 Parabolic Equations Minimising Linear Growth Functionate: L2 Theory 163
6.1 Introduction 163
6.2 Preliminaries 167
6.3 The Existence and Uniqueness Result 171
6.4 Strong Solution for Data in L2(fi) 173
6.5 Asymptotic Behaviour 199
6.6 Proof of the Approximation Lemma 200
7 Parabolic Equations Minimizing Linear Growth Functionals: L1 Theory 213
7.1 Introduction 213
7.2 The Main Result 216
7.3 The Semigroup Solution 217
7.4 Existence and Uniqueness for Data in L1(f2) 232
7.5 A Remark for Strictly Convex Lagrangians 264
7.6 The Cauchy Problem 268
Appendix
A Nonlinear Semigroups 271
A.I Introduction 271
A.2 Abstract Cauchy Problems 272
A.3 Mild Solutions 275
A.4 Accretive Operators 278
A.5 Existence and Uniqueness Theorem 285
A.6 Regularity of Mild Solutions 290
A.7 Completely Accretive Operators 291
Contents ix
B Functions of Bounded Variation 297
B.I Definitions 297
B.2 Approximation by Smooth Functions 298
B.3 Traces and Extensions 300
B.4 Sets of Finite Perimeter and the Coarea Formula 301
B.5 Some Isoperimetric Inequalities 302
B.6 The Reduced Boundary 303
B.7 Connected Components of Sets of Finite Perimeter 305
C Pairings Between Measures and Bounded Functions 311
C.I Trace of the Normal Component of Certain Vector Fields 311
C.2 The Measure {z,Du) 314
C.3 Representation of the Radon Nikodym Derivative 9(z, Du, •) . . . 317
Bibliography 323
Index 339
|
| any_adam_object | 1 |
| author | Andreu-Vaillo, Fuensanta 1955-2008 |
| author_GND | (DE-588)135629896 (DE-588)135629985 (DE-588)135630029 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| indexdate | 2024-07-09T19:58:35Z |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Andreu-Vaillo, Fuensanta 1955-2008 Verfasser (DE-588)135629896 aut Parabolic quasilinear equations minimizing linear growth functionals Fuensanta Andreu-Vaillo ; Vicent Caselles ; José M. Mazón Basel Birkhäuser 2004 XIV, 340 S. Ill. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 223 Includes bibliographical references and index Différences finies Equações diferenciais parciais parabólicas larpcal Opérateurs non linéaires Traitement d'images - Mathématiques Équations différentielles non linéaires Équations différentielles paraboliques Mathematik Differential equations, Nonlinear Differential equations, Parabolic Finite differences Image processing Mathematics Nonlinear operators Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Nichtlinearer Operator (DE-588)4225824-8 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s Nichtlinearer Operator (DE-588)4225824-8 s DE-604 Caselles, Vicent 1960- Sonstige (DE-588)135629985 oth Mazón, José M. 1953- Sonstige (DE-588)135630029 oth Progress in mathematics 223 (DE-604)BV000004120 223 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012828465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andreu-Vaillo, Fuensanta 1955-2008 Parabolic quasilinear equations minimizing linear growth functionals Progress in mathematics Différences finies Equações diferenciais parciais parabólicas larpcal Opérateurs non linéaires Traitement d'images - Mathématiques Équations différentielles non linéaires Équations différentielles paraboliques Mathematik Differential equations, Nonlinear Differential equations, Parabolic Finite differences Image processing Mathematics Nonlinear operators Parabolische Differentialgleichung (DE-588)4173245-5 gnd Nichtlinearer Operator (DE-588)4225824-8 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4173245-5 (DE-588)4225824-8 (DE-588)4205536-2 |
| title | Parabolic quasilinear equations minimizing linear growth functionals |
| title_auth | Parabolic quasilinear equations minimizing linear growth functionals |
| title_exact_search | Parabolic quasilinear equations minimizing linear growth functionals |
| title_full | Parabolic quasilinear equations minimizing linear growth functionals Fuensanta Andreu-Vaillo ; Vicent Caselles ; José M. Mazón |
| title_fullStr | Parabolic quasilinear equations minimizing linear growth functionals Fuensanta Andreu-Vaillo ; Vicent Caselles ; José M. Mazón |
| title_full_unstemmed | Parabolic quasilinear equations minimizing linear growth functionals Fuensanta Andreu-Vaillo ; Vicent Caselles ; José M. Mazón |
| title_short | Parabolic quasilinear equations minimizing linear growth functionals |
| title_sort | parabolic quasilinear equations minimizing linear growth functionals |
| topic | Différences finies Equações diferenciais parciais parabólicas larpcal Opérateurs non linéaires Traitement d'images - Mathématiques Équations différentielles non linéaires Équations différentielles paraboliques Mathematik Differential equations, Nonlinear Differential equations, Parabolic Finite differences Image processing Mathematics Nonlinear operators Parabolische Differentialgleichung (DE-588)4173245-5 gnd Nichtlinearer Operator (DE-588)4225824-8 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Différences finies Equações diferenciais parciais parabólicas Opérateurs non linéaires Traitement d'images - Mathématiques Équations différentielles non linéaires Équations différentielles paraboliques Mathematik Differential equations, Nonlinear Differential equations, Parabolic Finite differences Image processing Mathematics Nonlinear operators Parabolische Differentialgleichung Nichtlinearer Operator Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012828465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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