Multiple valued maps into a separable Hilbert space that almost minimize their $p$ Dirichlet energy or are squeeze and squash stationary

Philippe Bouafia; Thierry De Pauw; Changyou Wang

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arXiv · 1402.3232

Multiple valued maps into a separable Hilbert space that almost minimize their $p$ Dirichlet energy or are squeeze and squash stationary

Philippe Bouafia·Thierry De Pauw·Changyou Wang

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Abstract

Let $f : U\subset\Rm \to \calQ_Q(\ell_2)$ be of Sobolev class $W^{1,p}$, $1 < p < \infty$. If $f$ almost minimizes its $p$ Dirichlet energy then $f$ is H\"older continuous. If $p=2$ and $f$ is squeeze and squash stationary then $f$ is in VMO.

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Philippe Bouafia, Thierry De Pauw, Changyou Wang. 2014-02-13. Multiple valued maps into a separable Hilbert space that almost minimize their $p$ Dirichlet energy or are squeeze and squash stationary. https://arxiv.org/abs/1402.3232

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