Maps with prescribed tension fields

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We consider maps into Riemannian manifolds of non-positive curvature and start developing a systematic PDE theory. We control the Sobolev $H^{2,2}$-norm of such a map in terms of its energy, the $L^2$-norm of its tension field and a topological term depending on the homotopy class. We also solve a Dirchlet problem without an underlying variational structure, as an extension of the topic of harmonic maps with potentials.
To appear in Comm.Anal.Geom

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Differential Geometry, Analysis of PDEs, 58E20

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http://salesiana.dossiersoluciones.com/handle/123456789/69564

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312233
 http://arxiv.org/abs/math/0312233

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arXiv