Projects per year
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 |
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Pages (from-to) | 597-620 |
Number of pages | 620 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 51 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - Nov 2014 |
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Projects
- 1 Finished
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THE VARIATIONAL APPROACH TO BIHARMONIC MAPS
Engineering and Physical Sciences Research Council
1/09/09 → 28/02/13
Project: Research council