Answer: In additon to the heavy shade, the plants will also battle the tree for moisture and nutrients so odds for out and out success are very slim. For these reasons, you may discover that plants will grow in isolated spots rather than in a solid carpet. In my experience, too, it is worth trialing a variety of plants to see if any seem to respond better given the general growing conditions apart from the trees. Once you identify the best bet(s), then plant a larger area.
Epimedium is the best flowering candidate I can think of, but vinca minor (periwinkle) might do. A running form of Liriope is another possibility, although it can be very aggressive once it leaves the harsher conditions under the trees. Although not a blooming plant, English ivy might survive, and the variegated varieties such as the silver and blue-toned "Glacier" can be quite attractive. One other blooming groundcover plant you may hear mentioned for difficult situations is Bishop's Weed (Aegopodium). In all honesty I would urge you not to plant it as in my (sad) experience it too frequently escapes and becomes a nearly ineradicable weed. Good luck with your experiment!
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