\newcommand\Div{\operatorname{div}}
\newcommand\hl{\operatorname*{\star-lim'sup}}
\DeclareMathOperator\curl{curl}
\DeclareMathOperator*\argmax{argmax}
\begin{cases}
\Div_x u \Div^x u\Div_x^y u \Div^y_x u & \text{operatorname}\\
\hl_{x\to0} u \hl^w u \hl_{x\to0}^w u \hl^w_{x\to0} u & \text{operatorname*}\\
\hl\nolimits_{x\to0} u \hl\nolimits^w u
\hl\nolimits_{x\to0}^w u \hl\nolimits^w_{x\to0} u & \text{operatorname*:nolimits}\\
\curl_x v \argmax_K u & \text{DeclareMathOperator}
\end{cases}
