Generally trees don't belong in a perennial border,
but sometimes the circumstances dictate it. Here are some ways for you to deal with it.
Dig an 18" deep trench around 5 to 7' away from the trunk.
This particular tree is Salix babylonica 'Yatsubusa'
In the trench lay a root barrier that is impregnated with a chemical that will keep the roots in check.
For the complete story head over to Jenks Farmer's blog
Each year around this time we reduce and thin the tree and also enhance the weepiness of the tree by removing most of the vertical branches and tipping branches which results in weepy new growth in the spring.
Look how much we removed. A good rule of thumb is to never remove more than 30% of the canopy in one pruning.
The finished product
Adenophora liliifolia
Chinese Toadflax seeded in over top Violas, Alliums, and Purple Milk Thistles