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

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

Analysis of PDEs 2014-02-14 v1 Differential Geometry

Authors: Philippe Bouafia , Thierry De Pauw , Changyou Wang

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.

Keywords

multiple valued maps separable Hilbert space p-Dirichlet energy almost minimizers Hölder continuity squeeze and squash stationary VMO Sobolev class

Cite

@article{arxiv.1402.3232,
  title  = {Multiple valued maps into a separable Hilbert space that almost minimize their $p$ Dirichlet energy or are squeeze and squash stationary},
  author = {Philippe Bouafia and Thierry De Pauw and Changyou Wang},
  journal= {arXiv preprint arXiv:1402.3232},
  year   = {2014}
}

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25 pages

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

Abstract

Keywords

Cite

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