Quantitative stratification and higher regularity for biharmonic maps

Christine Breiner; Tobias Lamm

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arXiv · 1410.5640

Quantitative stratification and higher regularity for biharmonic maps

Christine Breiner·Tobias Lamm

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Abstract

In this paper we prove quantitative regularity results for stationary and minimizing extrinsic biharmonic maps. As an application, we determine sharp, dimension independent $L^p$ bounds for $\nabla^k f$ that do not require a small energy hypothesis. In particular, every minimizing biharmonic map is in $W^{4,p}$ for all $1\le p<5/4$. Further, for minimizing biharmonic maps from $Ω\subset \mathbb{R}^5$, we determine a uniform bound on the number of singular points in a compact set. Finally, using dimension reduction arguments, we extend these results to minimizing and stationary biharmonic maps into special targets.

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Christine Breiner, Tobias Lamm. 2015-03-26. Quantitative stratification and higher regularity for biharmonic maps. https://arxiv.org/abs/1410.5640

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