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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 $f$ isH\"older continuous. If $p=2$ and $f$ is squeeze and squash stationary then $f$is in VMO.

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