I solved it in another way, because I have the impression the solution above is doing what was not asked, i.e. implementing a dhcp server.
I deleted the bind9 and dhcp3-server with
sudo aptitude remove bind9 dhcp3-server
and restarted networking with
sudo /etc/init.d/networking restart
I also changed the file /etc/NetworkManager/NetworkManager.conf. Its contents looks like:
[main]
plugins=ifupdown,keyfile
dns=dnsmasq
[ifupdown]
managed=true
After modifying this file, I had to restart the Network Manager service:
sudo service network-manager restart
Now the dhcp client seems to set the dns server to the one provided by dhcp.