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| HAL: hal-00365912, version 1 |
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| The characteristic Cauchy problem for Dirac fields on curved backgrounds |
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| Dietrich Hafner 1Jean-Philippe Nicolas 2 |
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| (2009-03-03) |
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| On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in $L^2$ and we give an explicit definition of the space of data on the light-cone producing a solution in $H^1$. The method is based on energy estimates following L. Hörmander. |
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| 1: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : FR2254 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 2: | Laboratoire de mathématiques de Brest (LM) |
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CNRS : UMR6205 – Université de Bretagne Occidentale - Brest – Institut Supérieur des Sciences et Technologies de Brest (ISSTB) |
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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Metric Geometry Mathematics/Mathematical Physics Physics/Mathematical Physics |
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| Goursat problem – Dirac equation – Lorentzian geometry – Regularity – Energy estimates |
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| Attached file list to this document: | ||||||||||
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| hal-00365912, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00365912 | |
| oai:hal.archives-ouvertes.fr:hal-00365912 | |
| From: Jean-Philippe Nicolas | |
| Submitted on: Wednesday, 4 March 2009 23:44:30 | |
| Updated on: Thursday, 5 March 2009 17:36:54 | |
