# Intrinsically p-biharmonic maps

### Reference:

Hornung, P. and Moser, R., 2014. Intrinsically p-biharmonic maps. Calculus of Variations and Partial Differential Equations, 51 (3-4), pp. 597-620.

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### Official URL:

http://dx.doi.org/10.1007/s00526-013-0688-3

### 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 $u : \Omega \to N$. This requires finding a definition for the intrinsic Hessian of maps u : \Omega \to 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.

### Details

 Item Type Articles Creators Hornung, P.and Moser, R. DOI 10.1007/s00526-013-0688-3 Departments Faculty of Science > Mathematical Sciences Publisher Statement p-biharmonic.pdf: The final publication is available at link.springer.com Refereed Yes Status Published ID Code 30378