Apache ReverseProxy settings for network camera

Question

I have no tried several different possibilities to setup a reverse proxy for a AXIS 213PTZ network camera on my Apache webserver to be able to access it via HTTPS.

If I use a named virtual host, like axis.example.com it works fine with this configuration:

<VirtualHost *:80>
        ServerName axis.example.com
        ProxyPass / http://192.168.1.15:80/
        ProxyPassReverse / http://192.168.1.15:80/
</VirtualHost>

But as my SSL certificate is only valid for www.example.com, i tried to setup a reverse proxy using the directory axis as follows:

ProxyPass /axis/ http://192.168.1.15:80/
ProxyPassReverse /axis/ http://192.168.1.15:80/

I also tried a more advanced one:

ProxyPass /axis/ http://192.168.1.15/
ProxyHTMLURLMap http://192.168.1.15 /axis
<Location /axis/>
        ProxyPassReverse  http://192.168.1.15/
        SetOutputFilter proxy-html
        ProxyHTMLURLMap /           /axis/
        ProxyHTMLURLMap /axis      /axis
</Location>

But it does not work and I assume it is because of the following: If I enter https://www.example.com/axis, the URL is rewritten to https://www.example.com/view/index.shtml, so without the /axis/ part. If I enter it manually then the password prompt from the camera is shown, but afterwards website not found.

Is there a way to tell Apache to rewrite the URL correctly or do I have to consider something special because the camera is using .shtml pages?