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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 $u : \Omega \to N$. 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.
Original language  English 

Pages (fromto)  597620 
Number of pages  620 
Journal  Calculus of Variations and Partial Differential Equations 
Volume  51 
Issue number  34 
DOIs  
Publication status  Published  Nov 2014 
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Projects
 1 Finished

THE VARIATIONAL APPROACH TO BIHARMONIC MAPS
Engineering and Physical Sciences Research Council
1/09/09 → 28/02/13
Project: Research council