Having several contexts declared in a <host> entry, the default context
( <context name=""> .. </context> )
does not give access to other contexts declared in that host entry:
myContext.Context("/other") will always return myContext.

server.xml code snippet:

<host name="myhost.mydomain">
    <Context path="" docBase="/myWebapps/test" crossContext="true" />
    <Context path="other" docBase="/myWebapps/other" crossContext="true" />
</host>

/myWebapps/test/index.jsp:
my context: <%= getServletContext() %>
other context: <%= getServletContext().getContext("/other")