updated typos pdes

Mathematics/5th/Advanced_topics_in_functional_analysis_and_PDEs/Advanced_topics_in_functional_analysis_and_PDEs.tex

@@ -311,7 +311,7 @@
     % now add the conclusions of the gagliardo theorem
     there is an embedding $W^{m,p}(\Omega)\hookrightarrow L^q(\Omega)$, where $\displaystyle\frac{1}{q}=\frac{1}{p}-\frac{m}{d}$. If $p>\frac{d}{m}$, then $W^{m,p}(\Omega)\hookrightarrow \mathcal{C}^{k-m,\theta}(\Omega)$, where $\theta=m-\frac{d}{p}-\ell$ and $\ell:=\left\lfloor m-\frac{d}{p}\right\rfloor$.
   \end{theorem}
-  \begin{theorem}[Reillich-Kondrachov's compactness theorem]
+  \begin{theorem}[Reillich-Kondrachov's compactness theorem]\label{ATFAPDE:reillich_kondrachov_compactness}
     Let $\Omega\subseteq \RR^d$ be a bounded domain with $\mathcal{C}^k$ boundary. Then, $\forall m\leq k$ we have:
     \begin{itemize}
       \item If $1\leq p<\frac{d}{m}$, $\forall r\in [p,q)$, where $\displaystyle\frac{1}{q}=\frac{1}{p}-\frac{m}{d}$, the embedding $W^{m,p}(\Omega)\hookrightarrow L^r(\Omega)$ is compact.