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I am trying to find either

  • a general solution
  • a non-trivial class of solutions

to the following equation:

\begin{equation} (D_i D_j + D_j D_i) 1 = s_{ij} \end{equation}

where $D_i = \partial_i - a_i$ is a derivative (I think), $s_{ij}$ is an arbitrary symmetric tensor, and 1 is just the real number. (By solution, I mean I am ideally looking for $a$ in terms of $s$.) If it helps, the answer can be valid only in 3 dimensions.

joel
  • 103
  • Your notation ${(i}D{j)}$ isn't standard, at least for me.. Could you expand a little what you mean by that. – Jean Marie May 07 '17 at 17:26
  • @JeanMarie That is not what the notation says, it says $D_i$ and $D_j$ separately. Edit, sorry it seems like it has just been edited :) – John Doe May 07 '17 at 17:30

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