[Tex/LaTex] To write this norm equation better

Question

I have this norm

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\lVert f \rVert_{L_{2}(\Omega)} = \text{sup}_{
\begin{cases} 
v \in L_{2}(\Omega) \\
v \not= 0
\end{cases}
}
\frac{|(f,v)|} {\lVert v \rVert_{L_{2}(\Omega)}}
\end{equation}
\end{document}

which looks like

In the Johnson book about Finite Element methods the regulations are under the suprenum.
However, I am not sure if this is the best way to present this.

How can you write this equation rigorously?

Answer 1

If you have many norms in your document, it's better to use mathtools for simplifying input. I also add a \normL macro defined with the help of xparse.

Note that the commands \abs and \norm (as well as \normL) accept an optional argument which can be \big, \Big, \bigg or \Bigg in order to resize the fences; they can also be followed by * to imply usage of \left and \right.

The most important part is, however, \substack:

\documentclass{article}
\usepackage{mathtools,xparse}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\NewDocumentCommand{\normL}{ s O{} m }{%
  \IfBooleanTF{#1}{\norm*{#3}}{\norm[#2]{#3}}_{L_2(\Omega)}%
}

\begin{document}
\begin{equation}
\norm{f}_{L_{2}(\Omega)} =
\sup_{\substack{v \in L_{2}(\Omega) \\ v \not= 0}}
  \frac{\abs{(f,v)}}{\norm{v}_{L_{2}(\Omega)}}
\end{equation}
% Simplified notation with \normL
\begin{equation}
\normL{f} =
\sup_{\substack{v \in L_{2}(\Omega) \\ v \not= 0}} \frac{\abs{(f,v)}}{\normL{v}}
\end{equation}
\end{document}