Intrinsically p-biharmonic maps |
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Authors: | Peter Hornung Roger Moser |
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Institution: | 1. Institut für Angewandte Mathematik, Universit?t Bonn, 53115?, Bonn, Germany 2. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK
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Abstract: | For a compact Riemannian manifold \(N\) , a domain \(\Omega \subset \mathbb {R}^m\) and for \(p\in (1, \infty )\) , we introduce an intrinsic version \(E_p\) of the \(p\) -biharmonic energy functional for maps \(u : \Omega \rightarrow N\) . This requires finding a definition for the intrinsic Hessian of maps \(u : \Omega \rightarrow N\) whose first derivatives are merely \(p\) -integrable. We prove, by means of the direct method, existence of minimizers of \(E_p\) within the corresponding intrinsic Sobolev space, and we derive a monotonicity formula. Finally, we also consider more general functionals defined in terms of polyconvex functions. |
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