Problem to Autheticate with my Full qualify Internet host name

I have bought a Domain (b.e.: www.mydomain.com) and I have a domino server installed in my office with a static ip.My Domino server use the same www.mydomain.com into the full qualify Internet host name field.

Also, I have a router and my domino server is installed into the LAN with an IP that no change.

I have got to connect from Internet to my domino server and I can see my published databases. This is not the problem.

My problem appear when I am trying to authenticate from the http://www.mydominio.com. Domino don’t display any error when I am using a correct user and password but I cannot access to the private database.

Nevertheless, I can do it correctly using the IP Instead of www.mydominio.com

What’s the problem?