1
$\begingroup$

Is it true that since the smooth forms are dense in the $L^2$ and $H^{1,2}$ sections of forms, we can extend the exterior derivative $d$ and its adjoint $d^*$ to this spaces?

  • 2
    Can you extend the usual derivative from $C^\infty(\mathbb R)$ to $L^2(\mathbb R)$?2012-08-19
  • 0
    $d$ is continuous so I would define it as $d(f)=\lim d(\psi_n )$ where $\psi_n \rightarrow f$ , $f \in L^2$ $\psi_n in C^\infty$2012-08-19
  • 1
    $d$ is continuous with respect to what topology on $C^\infty$? Why would the limit you are proposing to use as definition exist?2012-08-19
  • 0
    @MarianoSuárez-Alvarez: $H^{1,2}$ is the space of functions with _one_ square integrable derivative. Why do you unsettle the OP like that? As a side remark: your first comment, in my opinion, should read: can you extend the usual derivative to $H^{1,2}$2012-08-19
  • 0
    i was addressing *half* of the question...2012-08-19
  • 1
    [This answer](http://math.stackexchange.com/questions/178657/averaging-differential-forms/178894#178894) might be relevant.2012-08-19

0 Answers 0