increase space between brace and equation

Question

Using the package mathtools the output of this code

\[
     \begin{dcases*}
        l_{\epsilon} = (l_ul_d)^{1/2}\\
        l_k = min(l_u,l_k)
        \end{dcases*}
\]

is the following

Is there a way to increase the space between the brace and the equations?

Answer 1

If you want to increase spacing for all dcases environments, you can use the \renewcases command from mathtools. Here is an extremist example:

\documentclass{article}
\usepackage{mathtools}
\makeatletter
\renewcases{dcases}{\,}{%
 $\m@th\displaystyle{##}$\hfil}{$\m@th\displaystyle{##}$\hfil}{\lbrace\qquad}{.}
\makeatother

\begin{document}

\[ \frac{\partial f(x)}{\partial L_1} =
            \begin{dcases}
                \frac{1}{\rho } - 1, \quad & x<L_1 \\
                0, \quad & \text{otherwise.}
            \end{dcases} \]

\end{document} 

Answer 2

I realised while writing the question that these could be two options:

\[
     \begin{dcases*}
       \quad l_{\epsilon} = (l_ul_d)^{1/2}\\
        ~ l_k = min(l_u,l_k)
        \end{dcases*}
\]