Nonlocal diffusion and applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Cham]
Springer
[2016]
|
| Schriftenreihe: | Lecture notes of the Unione matematica italiana
20 |
| Schlagworte: | |
| Online-Zugang: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (XII, 155 Seiten, 26 illus., 23 illus. in color) |
| ISBN: | 9783319287393 |
| DOI: | 10.1007/978-3-319-28739-3 |
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Datensatz im Suchindex
| _version_ | 1804176206861434880 |
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| adam_text | NONLOCAL DIFFUSION AND APPLICATIONS
/ BUCUR, CLAUDIA
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
1 A PROBABILISTIC MOTIVATION.-1.1 THE RANDOM WALK WITH ARBITRARILY LONG
JUMPS
1.2 A PAYOFF MODEL.-2 AN INTRODUCTION TO THE FRACTIONAL LAPLACIAN.-2.1
PRELIMINARY NOTIONS
2.2 FRACTIONAL SOBOLEV INEQUALITY AND GENERALIZED COAREA FORMULA
2.3 MAXIMUM PRINCIPLE AND HARNACK INEQUALITY
2.4 AN S-HARMONIC FUNCTION
2.5 ALL FUNCTIONS ARE LOCALLY S-HARMONIC UP TO A SMALL ERROR
2.6 A FUNCTION WITH CONSTANT FRACTIONAL LAPLACIAN ON THE BALL
3 EXTENSION PROBLEMS
3.1 WATER WAVE MODEL
3.2 CRYSTAL DISLOCATION
3.3 AN APPROACH TO THE EXTENSION PROBLEM VIA THE FOURIER TRANSFORM
4 NONLOCAL PHASE TRANSITIONS
4.1 THE FRACTIONAL ALLEN-CAHN EQUATION
4.2 A NONLOCAL VERSION OF A CONJECTURE BY DE GIORGI
5 NONLOCAL MINIMAL SURFACES
5.1 GRAPHS AND S-MINIMAL SURFACES
5.2 NON-EXISTENCE OF SINGULAR CONES IN DIMENSION 2 5.3 BOUNDARY
REGULARITY
6 A NONLOCAL NONLINEAR STATIONARY SCHROEDINGER TYPE EQUATION
6.1 FROM THE NONLOCAL UNCERTAINTY PRINCIPLE TO A FRACTIONAL WEIGHTED
INEQUALITY
ALTERNATIVE PROOFS OF SOME RESULTS
A.1 ANOTHER PROOF OF THEOREM A.2 ANOTHER PROOF OF LEMMA 2.3
REFERENCES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
NONLOCAL DIFFUSION AND APPLICATIONS
/ BUCUR, CLAUDIA
: 2016
ABSTRACT / INHALTSTEXT
WORKING IN THE FRACTIONAL LAPLACE FRAMEWORK, THIS BOOK PROVIDES MODELS
AND THEOREMS RELATED TO NONLOCAL DIFFUSION PHENOMENA. IN ADDITION TO A
SIMPLE PROBABILISTIC INTERPRETATION, SOME APPLICATIONS TO WATER WAVES,
CRYSTAL DISLOCATIONS, NONLOCAL PHASE TRANSITIONS, NONLOCAL MINIMAL
SURFACES AND SCHROEDINGER EQUATIONS ARE GIVEN. FURTHERMORE, AN EXAMPLE
OF AN S-HARMONIC FUNCTION, ITS HARMONIC EXTENSION AND SOME INSIGHT INTO
A FRACTIONAL VERSION OF A CLASSICAL CONJECTURE DUE TO DE GIORGI ARE
PRESENTED. ALTHOUGH THE AIM IS PRIMARILY TO GATHER SOME INTRODUCTORY
MATERIAL CONCERNING APPLICATIONS OF THE FRACTIONAL LAPLACIAN, SOME OF
THE PROOFS AND RESULTS ARE NEW. THE WORK IS ENTIRELY SELF-CONTAINED, AND
READERS WHO WISH TO PURSUE RELATED SUBJECTS OF INTEREST ARE INVITED TO
CONSULT THE RICH BIBLIOGRAPHY FOR GUIDANCE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| discipline | Mathematik |
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| spelling | Bucur, Claudia Verfasser aut Nonlocal diffusion and applications Claudia Bucur, Enrico Valdinoci [Cham] Springer [2016] © 2016 1 Online-Ressource (XII, 155 Seiten, 26 illus., 23 illus. in color) txt rdacontent c rdamedia cr rdacarrier Lecture notes of the Unione matematica italiana 20 Mathematics Functional analysis Integral transforms Operational calculus Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Integral Transforms, Operational Calculus Functional Analysis Mathematik Valdinoci, Enrico 1974- Verfasser (DE-588)13181012X aut Erscheint auch als Druckausgabe 978-3-319-28738-6 Lecture notes of the Unione matematica italiana 20 (DE-604)BV035421262 20 https://doi.org/10.1007/978-3-319-28739-3 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961667&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961667&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Bucur, Claudia Valdinoci, Enrico 1974- Nonlocal diffusion and applications Lecture notes of the Unione matematica italiana Mathematics Functional analysis Integral transforms Operational calculus Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Integral Transforms, Operational Calculus Functional Analysis Mathematik |
| title | Nonlocal diffusion and applications |
| title_auth | Nonlocal diffusion and applications |
| title_exact_search | Nonlocal diffusion and applications |
| title_full | Nonlocal diffusion and applications Claudia Bucur, Enrico Valdinoci |
| title_fullStr | Nonlocal diffusion and applications Claudia Bucur, Enrico Valdinoci |
| title_full_unstemmed | Nonlocal diffusion and applications Claudia Bucur, Enrico Valdinoci |
| title_short | Nonlocal diffusion and applications |
| title_sort | nonlocal diffusion and applications |
| topic | Mathematics Functional analysis Integral transforms Operational calculus Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Integral Transforms, Operational Calculus Functional Analysis Mathematik |
| topic_facet | Mathematics Functional analysis Integral transforms Operational calculus Partial differential equations Calculus of variations Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Integral Transforms, Operational Calculus Functional Analysis Mathematik |
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