Skip to content

Commit

Permalink
Couple of very minor fixes
Browse files Browse the repository at this point in the history
  • Loading branch information
jirilebl committed Jul 9, 2022
1 parent 493c338 commit 96c0995
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions ca.tex
Original file line number Diff line number Diff line change
Expand Up @@ -14345,7 +14345,7 @@ \subsection{Mean-value property}

\begin{exercise}
Suppose $U \subset \C$ is open, $f \colon U \to \R$ is continuous, $p \in U$
and $f$ is harmonic on $U \setminus \{ p \}$. Prove that $f$ is in fact
and $f$ is harmonic on $U \setminus \{ p \}$. Prove that $f$ is, in fact,
harmonic on all of $U$.
\end{exercise}

Expand Down Expand Up @@ -14604,7 +14604,7 @@ \subsection{Harnack's inequality}
Let $U = \{z \in \C : -s < \Re z < s, -1 < \Im z < 1 \}$.
Compute an explicit constant $C$
(doesn't need to be optimal)
for this following $K$ for the general
for the following $K$ for the general
Harnack's inequality:
\smallskip
\begin{expartshor}{2}
Expand Down Expand Up @@ -15056,7 +15056,7 @@ \subsection{Schwarz reflection principle}
$f \colon \partial \D \setminus S \to \R$ is continuous and bounded.
By \exerciseref{exercise:dirichDwithsings}, a continuous $g \colon
\overline{\D} \setminus S \to \R$ harmonic in $\D$ exists such that $g=f$ on
$\partial D \setminus S$. Prove that there is a unique such bounded $g$.
$\partial \D \setminus S$. Prove that there is a unique such bounded $g$.
Hint: Part a) and Cayley.
\end{exparts}
\end{exercise}
Expand Down

0 comments on commit 96c0995

Please sign in to comment.