APPROXIMATION IN FRACTIONAL SOBOLEV SPACES AND HODGE SYSTEMS

@inproceedings{Bousquet2017APPROXIMATIONIF,
  title={APPROXIMATION IN FRACTIONAL SOBOLEV SPACES AND HODGE SYSTEMS},
  author={Pierre Bousquet and Emmanuel Russ and Yi Wang and P Ver{\'o}nica Yung},
  year={2017}
}
  • Pierre Bousquet, Emmanuel Russ, +1 author P Verónica Yung
  • Published 2017
  • Mathematics
  • Let $d\geq 2$ be an integer, $1\leq l\leq d-1$ and $\varphi$ be a differential $l$-form on $\R^d$ with $\dot{W}^{1,d}$ coefficients. It was proved by Bourgain and Brezis that there exists a differential $l$-form $\psi$ on $\R^d$ with coefficients in $L^{\infty}\cap \dot{W}^{1,d}$ such that $d\varphi=d\psi$. Bourgain and Brezis also asked whether this result can be extended to differential forms with coefficients in the fractional Sobolev space $\dot{W}^{s,p}$ with $sp=d$. We give a positive… CONTINUE READING