From 680e1e763b8d899b3601b5ab0cf6f1fc2a114e1d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 3 Jun 2021 18:51:36 +0200
Subject: phases

---
 vorlesungen/slides/2/hilbertraum/sobolev.tex | 23 +++++++++++++----------
 1 file changed, 13 insertions(+), 10 deletions(-)

(limited to 'vorlesungen/slides/2/hilbertraum/sobolev.tex')

diff --git a/vorlesungen/slides/2/hilbertraum/sobolev.tex b/vorlesungen/slides/2/hilbertraum/sobolev.tex
index 425c263..828d34d 100644
--- a/vorlesungen/slides/2/hilbertraum/sobolev.tex
+++ b/vorlesungen/slides/2/hilbertraum/sobolev.tex
@@ -14,34 +14,37 @@
 \begin{block}{Vektorrraum $W$}
 Funktionen $f\colon \Omega\to\mathbb{C}$
 \begin{itemize}
-\item
+\item<2->
 $f\in L^2(\Omega)$
-\item
+\item<3->
 $\nabla f\in L^2(\Omega)$
-\item
+\item<4->
 homogene Randbedingungen:
 $f_{|\partial \Omega}=0$
 \end{itemize}
 \end{block}
+\uncover<5->{%
 \begin{block}{Skalarprodukt}
 \begin{align*}
 \langle f,g\rangle_W
-&=
-\int_\Omega \overline{\nabla f}(x)\cdot\nabla g(x)\,d\mu(x)
+&\uncover<6->{=
+\int_\Omega \overline{\nabla f}(x)\cdot\nabla g(x)\,d\mu(x)}
 \\
-&\qquad + \int_{\Omega} \overline{f}(x)\,g(x)\,d\mu(x)
+&\uncover<7->{\qquad + \int_{\Omega} \overline{f}(x)\,g(x)\,d\mu(x)}
 \\
-&=\langle f,-\Delta g + g\rangle_{L^2(\Omega)}
+&\uncover<8->{=\langle f,-\Delta g + g\rangle_{L^2(\Omega)}}
 \end{align*}
-\end{block}
+\end{block}}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<9->{%
 \begin{block}{Vollständigkeit}
 \dots
-\end{block}
+\end{block}}
+\uncover<10->{%
 \begin{block}{Anwendung}
 ``Ein Hilbertraum für jedes partielle Differentialgleichungsproblem''
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
 \end{frame}
-- 
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