Nonlinear elliptic equations and nonassociative algebras:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 200 |
| Schlagworte: |
Nonassociative rings and algebras
> Jordan algebras (algebras, triples and pairs)
> Jordan algebras (algebras, triples and pairs)
Nonassociative rings and algebras
> Other nonassociative rings and algebras
> Other nonassociative rings and algebras
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vii, 240 Seiten |
| ISBN: | 9781470417109 |
Internformat
MARC
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| 100 | 1 | |a Nadirašvili, Nikolai |d 1955- |e Verfasser |0 (DE-588)1066454159 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear elliptic equations and nonassociative algebras |c Nikolai Nadirashvili ; Vladimir Tkachev ; Serge Vlăduţ |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2014] | |
| 264 | 4 | |c © 2014 | |
| 300 | |a vii, 240 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 200 | |
| 650 | 4 | |a Jordan algebras | |
| 650 | 4 | |a Nonassociative rings | |
| 650 | 4 | |a Differential equations, Elliptic | |
| 650 | 4 | |a Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan algebras (algebras, triples and pairs) | |
| 650 | 4 | |a Nonassociative rings and algebras -- Other nonassociative rings and algebras -- Other nonassociative rings and algebras | |
| 650 | 4 | |a Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations | |
| 650 | 4 | |a Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | |
| 650 | 4 | |a Nonassociative rings and algebras -- General nonassociative rings -- Division algebras | |
| 650 | 4 | |a Calculus of variations and optimal control / optimization -- Manifolds -- Minimal surfaces | |
| 650 | 4 | |a Differential geometry -- Global differential geometry -- Calibrations and calibrated geometries | |
| 650 | 0 | 7 | |a Nichtassoziative Algebra |0 (DE-588)4297760-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare elliptische Differentialgleichung |0 (DE-588)4310554-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare elliptische Differentialgleichung |0 (DE-588)4310554-3 |D s |
| 689 | 0 | 1 | |a Nichtassoziative Algebra |0 (DE-588)4297760-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tkačev, Vladimir G. |d 1963- |e Verfasser |0 (DE-588)1067790888 |4 aut | |
| 700 | 1 | |a Vlăduţ, Serge G. |d 1954- |e Verfasser |0 (DE-588)1047955652 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-2045-1 |
| 830 | 0 | |a Mathematical surveys and monographs |v Volume 200 |w (DE-604)BV000018014 |9 200 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028040551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028040551 | ||
Datensatz im Suchindex
| _version_ | 1804174777722601472 |
|---|---|
| adam_text | Contents
Preface v
Chapter 1. Nonlinear Elliptic Equations 1
1.1. Elliptic equations 1
1.2. Viscosity solutions 8
1.3. Linear elliptic operators of nondivergence form 11
1.4. Nonlinear equations with smooth solutions 16
1.5. Degenerate elliptic equations 22
1.6. Homogeneous solutions 27
1.7. Liouville type theorems. Removable singularities 38
Chapter 2. Division Algebras, Exceptional Lie Groups, and Calibrations 45
2.1. The Cayley-Dickson construction. Octonions 46
2.2. Clifford algebras and spinor groups 48
2.3. The group G2. Trialities 51
2.4. Cross products, associative and coassociative calibrations 53
2.5. Cross products, normed algebras, and Cayley calibrations 58
Chapter 3. Jordan Algebras and the Cartan Isoparametric Cubics 63
3.1. Isoparametric cubics and the eiconal equation 63
3.2. Jordan algebras 67
3.3. The eiconal equation and cubic Jordan algebras 77
Chapter 4. Solutions from Trialities 85
4.1. The simplest nonclassical construction 85
4.2. The octonionic construction 96
4.3. Hessian equations in twelve dimensions 104
4.4. Isaacs equations 114
Chapter 5. Solutions from Isoparametric Forms 117
5.1. The spectrum 117
5.2. Nonclassical and singular solutions 125
5.3. Singular solutions in five dimensions 132
5.4. Other isoparametric forms 143
5.5. Two more applications 150
Chapter 6- Cubic Minimal Cones 155
6.1. Brief overview of the main results 155
6-2. Algebraic minimal hypercones in Rn and radial eigencubics 159
6.3. Metrized and FYeudenthal Springer algebras 161
6.4. Radial eigencubic algebras 163
iii
IV
CONTENTS
6.5. Polar and Clifford REC algebras 169
6.6. The harmonicity of radial eigencubics 176
6.7. The Peirce decomposition of a REC algebra 180
6.8. Triality systems and a hidden Clifford algebra structure 185
6.9. Jordan algebra V* 189
6.10. Reducible REC algebras 194
6.11. Exceptional REC algebras 198
Chapter 7. Singular Solutions in Calibrated Geometries 205
7.1. Calibrated geometries 205
7.2. Singular coassociative 4֊folds 209
7.3. Singular solutions of special Lagrangian equations 211
7.4. More singular solutions and a failure of the maximum principle 218
Bibliography 223
Notation 235
Index 239
|
| any_adam_object | 1 |
| author | Nadirašvili, Nikolai 1955- Tkačev, Vladimir G. 1963- Vlăduţ, Serge G. 1954- |
| author_GND | (DE-588)1066454159 (DE-588)1067790888 (DE-588)1047955652 |
| author_facet | Nadirašvili, Nikolai 1955- Tkačev, Vladimir G. 1963- Vlăduţ, Serge G. 1954- |
| author_role | aut aut aut |
| author_sort | Nadirašvili, Nikolai 1955- |
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| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)903300485 (DE-599)BSZ424574888 |
| dewey-full | 512.48 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.48 |
| dewey-search | 512.48 |
| dewey-sort | 3512.48 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042607613 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:05:47Z |
| institution | BVB |
| isbn | 9781470417109 |
| language | English |
| lccn | 2014028806 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028040551 |
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| physical | vii, 240 Seiten |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Nadirašvili, Nikolai 1955- Verfasser (DE-588)1066454159 aut Nonlinear elliptic equations and nonassociative algebras Nikolai Nadirashvili ; Vladimir Tkachev ; Serge Vlăduţ Providence, Rhode Island American Mathematical Society [2014] © 2014 vii, 240 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 200 Jordan algebras Nonassociative rings Differential equations, Elliptic Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan algebras (algebras, triples and pairs) Nonassociative rings and algebras -- Other nonassociative rings and algebras -- Other nonassociative rings and algebras Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) Nonassociative rings and algebras -- General nonassociative rings -- Division algebras Calculus of variations and optimal control / optimization -- Manifolds -- Minimal surfaces Differential geometry -- Global differential geometry -- Calibrations and calibrated geometries Nichtassoziative Algebra (DE-588)4297760-5 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s Nichtassoziative Algebra (DE-588)4297760-5 s DE-604 Tkačev, Vladimir G. 1963- Verfasser (DE-588)1067790888 aut Vlăduţ, Serge G. 1954- Verfasser (DE-588)1047955652 aut Erscheint auch als Online-Ausgabe 978-1-4704-2045-1 Mathematical surveys and monographs Volume 200 (DE-604)BV000018014 200 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028040551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nadirašvili, Nikolai 1955- Tkačev, Vladimir G. 1963- Vlăduţ, Serge G. 1954- Nonlinear elliptic equations and nonassociative algebras Mathematical surveys and monographs Jordan algebras Nonassociative rings Differential equations, Elliptic Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan algebras (algebras, triples and pairs) Nonassociative rings and algebras -- Other nonassociative rings and algebras -- Other nonassociative rings and algebras Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) Nonassociative rings and algebras -- General nonassociative rings -- Division algebras Calculus of variations and optimal control / optimization -- Manifolds -- Minimal surfaces Differential geometry -- Global differential geometry -- Calibrations and calibrated geometries Nichtassoziative Algebra (DE-588)4297760-5 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| subject_GND | (DE-588)4297760-5 (DE-588)4310554-3 |
| title | Nonlinear elliptic equations and nonassociative algebras |
| title_auth | Nonlinear elliptic equations and nonassociative algebras |
| title_exact_search | Nonlinear elliptic equations and nonassociative algebras |
| title_full | Nonlinear elliptic equations and nonassociative algebras Nikolai Nadirashvili ; Vladimir Tkachev ; Serge Vlăduţ |
| title_fullStr | Nonlinear elliptic equations and nonassociative algebras Nikolai Nadirashvili ; Vladimir Tkachev ; Serge Vlăduţ |
| title_full_unstemmed | Nonlinear elliptic equations and nonassociative algebras Nikolai Nadirashvili ; Vladimir Tkachev ; Serge Vlăduţ |
| title_short | Nonlinear elliptic equations and nonassociative algebras |
| title_sort | nonlinear elliptic equations and nonassociative algebras |
| topic | Jordan algebras Nonassociative rings Differential equations, Elliptic Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan algebras (algebras, triples and pairs) Nonassociative rings and algebras -- Other nonassociative rings and algebras -- Other nonassociative rings and algebras Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) Nonassociative rings and algebras -- General nonassociative rings -- Division algebras Calculus of variations and optimal control / optimization -- Manifolds -- Minimal surfaces Differential geometry -- Global differential geometry -- Calibrations and calibrated geometries Nichtassoziative Algebra (DE-588)4297760-5 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| topic_facet | Jordan algebras Nonassociative rings Differential equations, Elliptic Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan algebras (algebras, triples and pairs) Nonassociative rings and algebras -- Other nonassociative rings and algebras -- Other nonassociative rings and algebras Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) Nonassociative rings and algebras -- General nonassociative rings -- Division algebras Calculus of variations and optimal control / optimization -- Manifolds -- Minimal surfaces Differential geometry -- Global differential geometry -- Calibrations and calibrated geometries Nichtassoziative Algebra Nichtlineare elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028040551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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