Looking for \mathbb style $\Delta$ and $\nabla$

Here's a possible workaround if the symbols aren't available:

Use the relevant symbol, say \Delta with negative kerning, say, \mkern-12u and the same symbol again.

The kerning value is just a guess and can be changed of course.

The package bbold provides a blackboard letter symbol for \Delta, but this looks different and is probably not desired.

The mbboard package seems to define the symbols out of the box, but it is not on TeXLive, see mbboard on CTAN.

\documentclass{article}


\usepackage{bbm}
\usepackage{mathtools}
\usepackage{bbold}


\newcommand{\bbDelta}{%
  \Delta\mkern-12mu\Delta%
}

\newcommand{\bbNabla}{%
  \nabla\mkern-12mu\nabla%
}

\begin{document}

The symbol \verb!\mathbb{\Delta}!  $\mathbb{\Delta}$ is probably wrong. 


Some testing of symbols
\verb!\normalsize:!\normalsize

$\bbDelta$ and $\bbNabla$

\verb!\large:!\large

$\bbDelta$ and $\bbNabla$

\verb!\Large:!\Large

$\bbDelta$ and $\bbNabla$

\verb!\LARGE:!\LARGE

$\bbDelta$ and $\bbNabla$

\verb!\huge:!\huge

$\bbDelta$ and $\bbNabla$


\normalsize
\[
   \bbDelta \neq \bbNabla
\]


\end{document}


[![enter image description here][1]][1]

You can find the definitions employed by the paper's author by downloading the source file from arXiv.

Those two symbols are there defined as:

\newcommand{\DD}{\Delta\!\!\!\!\Delta}
\newcommand{\Grad}{\nabla\!\!\!\!\nabla}

Note that this might not be the best way to define symbols like those -- it's just the way used by the author -- and other answers here can provide better definitions.

Run with xelatex or lualatex:

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\def\dDelta{\upDelta\mkern-10mu\upDelta}
\def\dNabla{\nabla\mkern-10mu\nabla}
\begin{document}

\Huge$\dDelta$ and $\dNabla$

\end{document}

If you want the bold characters use \mbfDelta and \mbfnabla instead.