Cannot get hyperlinks in elsart.cls documents

When formatting a document with the class elsart.cls provided by Elsevier, hyperlinks to sections, equations, items... don't work.

I know that elsart.cls is supposed to be obsoleted by elsarticle (most notably, it is not in CTAN anymore, while elsarticle is). But some journals still require it (read "they provide an add-on package which fails with a lot of errors if used with elsarticle instead of elsart ").

MWE:

\documentclass{elsart}

\usepackage{hyperref}

\begin{document}

\begin{frontmatter}
  \title{The title}
  \author{The author}
  \address{The address}

  \begin{abstract}
    ...
  \end{abstract}

\end{frontmatter}

\section{Section}
\label{sec1}

This is a reference without an hyperlink: \ref{sec1}

\end{document}

I hope the tagging is appropriate: the tag elsart did not exist, but this question is specifically about elsart, excluding elsarticle...