Transport Equations and Multi-D Hyperbolic Conservation Laws
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| Sprache: | English |
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2008
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| Schriftenreihe: | Lecture notes of the Unione Matematica Italiana
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| Online-Zugang: | DE-634 DE-91 DE-384 DE-703 DE-29 DE-739 Volltext Inhaltsverzeichnis |
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Datensatz im Suchindex
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| adam_text | CONTENTS PARTI EXISTENCE, UNIQUENESS, STABILITY AND DIFFERENTIABILITY
PROPERTIES OF THE FLOW ASSOCIATED TO WEAKLY DIFFERENTIABLE VECTOR FIELDS
3 LUIGI AMBROSIO AND GIANLUCA CRIPPA 1 INTRODUCTION 3 2 THE CONTINUITY
EQUATION 5 3 THE CONTINUITY EQUATION WITHIN THE CAUCHY-LIPSCHITZ
FRAMEWORK 7 4 (ODE) UNIQUENESS VS. (PDE) UNIQUENESS 11 5 THE FLOW
ASSOCIATED TO SOBOLEV OR BV VECTOR FIELDS 19 6 MEASURE-THEORETIC
DIFFERENTIALS 32 7 DIFFERENTIABILITY OF THE FLOW IN THE W L 1 CASE 38
8 DIFFERENTIABILITY AND COMPACTNESS OF THE FLOW IN THE W LP CASE 40 9
BIBLIOGRAPHICAL NOTES AND OPEN PROBLEMS 52 REFERENCES 54 PARTLL A NOTE
ON ALBERTI S RANK-ONE THEOREM 61 CAMILLO DE LELLIS 1 INTRODUCTION 61 2
DIMENSIONAL REDUCTION 63 3 A BLOW-UP ARGUMENT LEADING TO A PARTIAL
RESULT 65 4 THE FUNDAMENTAL LEMMA 66 5 PROOF OF THEOREM 1.1 IN THE
PLANAR CASE 68 REFERENCES 74 GESCANNT DURCH BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/987389114 DIGITALISIERT DURCH EXISTENCE,
UNIQUENESS, STABILITY AND DIFFERENTIABILITY PROPERTIES OF THE FLOW
ASSOCIATED TO WEAKLY DIFFERENTIABLE VECTOR FIELDS LUIGI AMBROSIO AND
GIANLUCA CRIPPA SCUOLA NORMALE SUPERIORE, PIAZZA DEI CAVALIERI 7, 56126
PISA, ITALY E-MAIL: L.AMBROSIO@SNS.IT, G.CRIPPA@SNS.IT URL:
HTTP://CVGMT.SNS.IT/PEOPLE/AMBROSIO/ 1 INTRODUCTION 3 2 THE CONTINUITY
EQUATION 5 3 THE CONTINUITY EQUATION WITHIN THE CAUCHY*LIPSCHITZ
FRAMEWORK 7 4 (ODE) UNIQUENESS VS. (PDE) UNIQUENESS 11 5 THE FLOW
ASSOCIATED TO SOBOLEV OR BV VECTOR FIELDS 19 6 MEASURE-THEORETIC
DIFFERENTIALS 32 7 DIFFERENTIABILITY OF THE FLOW IN THE W M CASE 38 8
DIFFERENTIABILITY AND COMPACTNESS OF THE FLOW IN THE W L * CASE 40 9
BIBLIOGRAPHICAL NOTES AND OPEN PROBLEMS 52 REFERENCES 54 REFERENCES 74 A
NOTE ON ALBERTI S RANK-ONE THEOREM CAMILLO DE LELLIS INSTITUT
FURMATHEMATIK, UNIVERSITAT ZURICH, WINTERTHURERSTRASSE 190, CH-8057
ZURICH, SWITZERLAND E-MAIL: DELELLIS@MATH.UNIZH.CH URL:
HTTP://WWW.MATH.UNIZH.CH/ 1 INTRODUCTION 61 2 DIMENSIONAL REDUCTION 63 3
A BLOW-UP ARGUMENT LEADING TO A PARTIAL RESULT 65 4 THE FUNDAMENTAL
LEMMA 66 5 PROOF OF THEOREM 1.1 IN THE PLANARCASE 68 77 REGULARIZING
EFFECT OF NONLINEARITY IN MULTIDIMENSIONAL SCALAR CONSERVATION LAWS
GIANLUCA CRIPPA 1 , FELIX OTTO 2 , AND MICHAEL WESTDICKENBERG 3 SCUOLA
NORMALE SUPERIORE, PIAZZA DEI CAVALIERI 7,1-56126 PISA, ITALY E-MAIL:
G.CRIPPA@SNS.IT 2 INSTIRUT FUR ANGEWANDTE MATHEMATIK, UNIVERSITAT BONN,
WEGELERSTRABE 10, D-53115 BONN, GERMANY E-MAIL: OTTO@IAM.UNI-BONN.DE 3
SCHOOL OF MATHEMATICS, GEORGIA INSTITUTE OF TECHNOLOGY, 686 CHERRY
STREET, ATLANTA, GEORGIA 30332-0160, U.S.A. E-MAIL:
MWEST@MATH.GATECH.EDU URL: HTTP://WWW.MATHPHYS.IAM.UNIBONN.DE/~OTTO/
URL: HTTP://WWW.MATH.GATECH.EDU/~MWEST/ 1 INTRODUCTION 77 2 BACKGROUND
MATERIAL 79 3 ENTROPY SOLUTIONS WITH BV-REGULARIRY 84 4 STRUCTURE OF
ENTROPY SOLUTIONS 87 5 KINETIC FORMULATION, BLOW-UPS AND SPLIT STATES 91
6 CLASSIFICATION OF SPLIT STATES 98 6.1 SPECIAL SPLIT STATES: NO ENTROPY
DISSIPATION 98 6.2 SPECIAL SPLIT STATES: V SUPPORTED ON A HYPERPLANE 101
6.3 SPECIAL SPLIT STATES: V SUPPORTED ON HAIFA HYPERPLANE 103 6.4
CLASSIFICATION OF GENERAL SPLIT STATES 105 7 PROOF OF THE MAIN THEOREM
106 8 PROOFS OF THE REGULARITY THEOREMS 112 REFERENCES 127
|
| any_adam_object | 1 |
| author | Ambrosio, Luigi 1963- |
| author_GND | (DE-588)133791408 (DE-588)1044329165 (DE-588)135534305 (DE-588)122562321 |
| author_facet | Ambrosio, Luigi 1963- |
| author_role | aut |
| author_sort | Ambrosio, Luigi 1963- |
| author_variant | l a la |
| building | Verbundindex |
| bvnumber | BV036492402 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)1184394301 (DE-599)BVBBV036492402 |
| dewey-full | 515.3535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3535 |
| dewey-search | 515.3535 |
| dewey-sort | 3515.3535 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-540-76781-7 |
| format | Electronic eBook |
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| id | DE-604.BV036492402 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T00:05:38Z |
| institution | BVB |
| isbn | 9783540767817 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020414991 |
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| physical | 1 Online-Ressource |
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| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer-Verlag Berlin Heidelberg |
| record_format | marc |
| series | Lecture notes of the Unione Matematica Italiana |
| series2 | Lecture notes of the Unione Matematica Italiana |
| spellingShingle | Ambrosio, Luigi 1963- Transport Equations and Multi-D Hyperbolic Conservation Laws Lecture notes of the Unione Matematica Italiana Mathematik Calculus of Variations and Optimal Control; Optimization Differential Equations Mathematics Measure and Integration Ordinary Differential Equations Partial Differential Equations Differential equations, partial Mathematical optimization Geometrische Maßtheorie (DE-588)4125258-5 gnd Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd |
| subject_GND | (DE-588)4125258-5 (DE-588)4228136-2 (DE-588)1071861417 |
| title | Transport Equations and Multi-D Hyperbolic Conservation Laws |
| title_auth | Transport Equations and Multi-D Hyperbolic Conservation Laws |
| title_exact_search | Transport Equations and Multi-D Hyperbolic Conservation Laws |
| title_full | Transport Equations and Multi-D Hyperbolic Conservation Laws by Luigi Ambrosio, Gianluca Crippa, Camillo Lellis, Felix Otto, Michael Westdickenberg |
| title_fullStr | Transport Equations and Multi-D Hyperbolic Conservation Laws by Luigi Ambrosio, Gianluca Crippa, Camillo Lellis, Felix Otto, Michael Westdickenberg |
| title_full_unstemmed | Transport Equations and Multi-D Hyperbolic Conservation Laws by Luigi Ambrosio, Gianluca Crippa, Camillo Lellis, Felix Otto, Michael Westdickenberg |
| title_short | Transport Equations and Multi-D Hyperbolic Conservation Laws |
| title_sort | transport equations and multi d hyperbolic conservation laws |
| topic | Mathematik Calculus of Variations and Optimal Control; Optimization Differential Equations Mathematics Measure and Integration Ordinary Differential Equations Partial Differential Equations Differential equations, partial Mathematical optimization Geometrische Maßtheorie (DE-588)4125258-5 gnd Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd |
| topic_facet | Mathematik Calculus of Variations and Optimal Control; Optimization Differential Equations Mathematics Measure and Integration Ordinary Differential Equations Partial Differential Equations Differential equations, partial Mathematical optimization Geometrische Maßtheorie Nichtlineare hyperbolische Differentialgleichung Konferenzschrift 2005 Bologna |
| url | https://doi.org/10.1007/978-3-540-76781-7 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020414991&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035421262 |
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