Boundaries of Graphs of Harmonic Functions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Boundaries of Graphs of Harmonic Functions
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| Creator |
Fox, D.
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| 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.
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| Date |
2019-02-19T17:36:22Z
2019-02-19T17:36:22Z 2009 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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