Harmonic fields on the extended projective disc and a problem in optics

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dc.creatorOtway, Thomas H.
dc.date2004-12-20
dc.date2007-04-02
dc.date.accessioned2026-07-07T07:56:37Z
dc.date.available2026-07-07T07:56:37Z
dc.descriptionThe Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for weakly harmonic 1-fields, changing type on the unit circle, is derived under Dirichlet conditions imposed on the non-characteristic portion of the boundary. A similar system arises in the analysis of wave motion near a caustic. A class of elliptic-hyperbolic boundary-value problems is formulated for those equations as well. For both classes of boundary-value problems, an arbitrarily small lower-order perturbation of the equations is shown to yield solutions which are strong in the sense of Friedrichs.
dc.description30 pages; Section 3.3 has been revised
dc.identifierhttps://arxiv.org/abs/math-ph/0412072
dc.identifierhttp://arxiv.org/abs/math-ph/0412072
dc.identifierJournal of Mathematical Physics 46, 113501 (2005), 21 pp
dc.identifierdoi:10.1063/1.2098529
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127371
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject35M10; 58J32; 53A20; 78A05
dc.titleHarmonic fields on the extended projective disc and a problem in optics
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