It sounds like it is graphical application which fails to access your $DISPLAY. So you need to make sure sudo preserves $DISPLAY environment variable and user root is allowed to access it. For the former look at /etc/sudoers and man sudoers, specifically env_keep. For the latter you can (for one off) just do xhost + or add pam_xauth to sudo PAM configuration or tell sudo to preserve $XAUTHORITY variable or do xhost +si:localuser:root and I am sure this list is not complete.