Maps with prescribed tension fields
Wenyi Chen, Juergen Jost
Abstract
We consider maps into Riemannian manifolds of non-positive curvature and start developing a systematic PDE theory. We control the Sobolev H2,2-norm of such a map in terms of its energy, the L2-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.
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