What question are you awaiting "the answer" for? Text formatting does not carry over in text variables.
Variables are treated as a single character for formatting, so they carry either the paragraph style of the paragraphe in which they are inserted or an assigned character style or override, but whatever is assigned, it applies uniformly to thentire variable string.
You can do it if you make a new master page and apply it to that section for the running heads that contain italics text.
You then make the text variable from Character Styles, and apply character styles to the headings.
IT's not ideal and may be more trouble than it's worth.
However, there is PowerHeaders from InTools which can do this. http://in-tools.com/products/plugins/power-headers/