Sorry... I communicated poorly before.
Your mana regen in combat is reduced to 20% of normal.
If you are wearing gear that increases your mana regen, then it is applied to this 20%... in other words, if your gear increases mana regen by 100% (doubles it), then the total regen you are getting in combat is still just 40% of normal non-combat regen. The short version of all of this is that mana regen gear is CRAP for combat purposes. If you wanted your combat regen to match your non-combat regen, you would need a total of +400% gear from robes, rings, etc. -- it's just not a good trade-off, and getting that much mana regen would take a long time to find/enchant yourself anyway.
A smarter way to go about this is to figure out what kind of schools you like using the most often, and getting gear that reduces the spell costs of that school -- for example, restoration gear that makes it easier to Heal, Turn Undead (lots of undead in this game), and Ward. Eventually, with a high enough Enchant skill, you will be able to make gear that reduces the spell costs of all spells from a school to ZERO. This is made easier with potions that temporarily increase your Enchanting skill while crafting said items for yourself. Imagine being able to heal indefinitely, cast an undraining Ward spell... this is what you can achieve with high-quality Restoration gear and powerful soul gems. If you get the Enchanting perk that lets you put two enchants per item, you can do this trick with 2 schools instead of one, basically meaning that you can cast almost half of the spells in the game for no mana cost! Free fireballs, infinite lightning bolts... fun stuff.

I know that a lot of folks dig Conjuration, and will do this trick with the Conjuration and Restoration schools, but it works for any of them.
-Loth