Multiple valued maps into a separable Hilbert space that almost minimize   their $p$ Dirichlet energy or are squeeze and squash stationary
  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. 
Philippe Bouafia, Thierry De Pauw, Changyou Wang
math.AP math.DG