Boundaries of Graphs of Harmonic Functions
Harmonic functions u: Rn → Rm are equivalent to integral manifolds of an exterior differential system with independence condition (M,I,ω). To this system one associates the space of conservation laws C. They provide necessary conditions for g: Sn–1 → M to be the boundary of an integral submanifold....
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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149134 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Boundaries of Graphs of Harmonic Functions / D. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. |
Репозитарії
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irk-123456789-1491342019-02-20T01:26:38Z Boundaries of Graphs of Harmonic Functions Fox, D. Harmonic functions u: Rn → Rm are equivalent to integral manifolds of an exterior differential system with independence condition (M,I,ω). To this system one associates the space of conservation laws C. They provide necessary conditions for g: Sn–1 → M to be the boundary of an integral submanifold. We show that in a local sense these conditions are also sufficient to guarantee the existence of an integral manifold with boundary g(Sn–1). The proof uses standard linear elliptic theory to produce an integral manifold G: Dn → M and the completeness of the space of conservation laws to show that this candidate has g(Sn–1) as its boundary. As a corollary we obtain a new elementary proof of the characterization of boundaries of holomorphic disks in Cm in the local case. 2009 Article Boundaries of Graphs of Harmonic Functions / D. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35J05; 35J25; 53B25 http://dspace.nbuv.gov.ua/handle/123456789/149134 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Harmonic functions u: Rn → Rm are equivalent to integral manifolds of an exterior differential system with independence condition (M,I,ω). To this system one associates the space of conservation laws C. They provide necessary conditions for g: Sn–1 → M to be the boundary of an integral submanifold. We show that in a local sense these conditions are also sufficient to guarantee the existence of an integral manifold with boundary g(Sn–1). The proof uses standard linear elliptic theory to produce an integral manifold G: Dn → M and the completeness of the space of conservation laws to show that this candidate has g(Sn–1) as its boundary. As a corollary we obtain a new elementary proof of the characterization of boundaries of holomorphic disks in Cm in the local case. |
| format |
Article |
| author |
Fox, D. |
| spellingShingle |
Fox, D. Boundaries of Graphs of Harmonic Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Fox, D. |
| author_sort |
Fox, D. |
| title |
Boundaries of Graphs of Harmonic Functions |
| title_short |
Boundaries of Graphs of Harmonic Functions |
| title_full |
Boundaries of Graphs of Harmonic Functions |
| title_fullStr |
Boundaries of Graphs of Harmonic Functions |
| title_full_unstemmed |
Boundaries of Graphs of Harmonic Functions |
| title_sort |
boundaries of graphs of harmonic functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149134 |
| citation_txt |
Boundaries of Graphs of Harmonic Functions / D. Fox // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 8 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT foxd boundariesofgraphsofharmonicfunctions |
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2023-05-20T17:32:23Z |
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2023-05-20T17:32:23Z |
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1796153523708100608 |