Commit 4290684e authored by Leonard Fisser's avatar Leonard Fisser 🐸
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Add \section to math slide

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......@@ -72,26 +72,25 @@
You can even have multiple footnotes\footnote{Hello again!}!
What about really long footnotes\footnote{Let's see how long we can make this footnote, just to make sure you can put everything you want here!}?
\end{frame}
\begin{frame}
\frametitle{Slide with Math}
Let $\Omega \subset \mathbb{R}^2$ be a bounded Lipschitz domain.
\begin{theorem}
For all $p \in \big[\frac{4}{3}, 4\big]$ and all $0 < \theta < 1$, the continuous embedding
\begin{align*}
\mathrm{H}^{2 \theta , p}_{0 , \sigma} (\Omega) \subset \mathcal{D}(A_p^{\theta})
\end{align*}
holds.
Furthermore, there exists $\delta \in (0 , 1]$ such that, if $\theta$ and $p$ additionally satisfy either
\begin{align*}
\theta < \frac{1}{2} + \frac{1}{2 p} \quad &\text{if} \quad \frac{1}{2} - \frac{1}{p} \leq \frac{\delta}{2} \qquad\text{or } \\
\theta < \frac{1}{p} + \frac{1 + \delta}{4} \quad &\text{if} \quad \frac{1}{2} - \frac{1}{p} > \frac{\delta}{2},
\end{align*}
we have with equivalent norms that $\mathcal{D}(A_p^{\theta}) = \mathrm{H}^{2 \theta , p}_{0 , \sigma} (\Omega).$
\end{theorem}
\begin{frame}{Slide with Math}
\section{Example: Math}
Let $\Omega \subset \mathbb{R}^2$ be a bounded Lipschitz domain.
\begin{theorem}
For all $p \in \big[\frac{4}{3}, 4\big]$ and all $0 < \theta < 1$, the continuous embedding
\begin{align*}
\mathrm{H}^{2 \theta , p}_{0 , \sigma} (\Omega) \subset \mathcal{D}(A_p^{\theta})
\end{align*}
holds.
Furthermore, there exists $\delta \in (0 , 1]$ such that, if $\theta$ and $p$ additionally satisfy either
\begin{align*}
\theta < \frac{1}{2} + \frac{1}{2 p} \quad &\text{if} \quad \frac{1}{2} - \frac{1}{p} \leq \frac{\delta}{2} \qquad\text{or } \\
\theta < \frac{1}{p} + \frac{1 + \delta}{4} \quad &\text{if} \quad \frac{1}{2} - \frac{1}{p} > \frac{\delta}{2},
\end{align*}
we have with equivalent norms that $\mathcal{D}(A_p^{\theta}) = \mathrm{H}^{2 \theta , p}_{0 , \sigma} (\Omega).$
\end{theorem}
\end{frame}
\finalpage
......
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