2
\documentclass[12pt]{article}
\usepackage{mathtools}
\begin{document}

\begin{equation}
\begin{rcases*}
 \left( \nabla^2+k^2\right) & u(\mathbf{r}) =0, \quad r > a \\
& u(\mathbf{r})  =0, \quad r=a.
\end{rcases*} 
\end{equation}

\end{document}
2

If you want the material after the & alignment points to be treated as being in math mode, use the rcases environment, not the rcases* environment:

enter image description here

\documentclass[12pt]{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{rcases}
 \left( \nabla^2+k^2\right) & u(\mathbf{r}) =0, \quad r > a \\
& u(\mathbf{r}) =0, \quad r=a.
\end{rcases} 
\end{equation}
\end{document}
0

I'm not sure about rcases, but do you want the following?

\documentclass[12pt]{article}
\usepackage{mathtools}
\begin{document}

\begin{equation} 
    \left( \nabla^2+k^2\right) \begin{cases}
    u(\mathbf{r}) =0,  & \quad r > a\\
 u(\mathbf{r}) =0, & \quad r=a
\end{cases}
\end{equation}

\end{document}

enter image description here

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