Eyebrows going away from eczema around eyebrows, how do I make them grow fast?

If one's atopic dermatitis is severe enough to prompt eyebrow loss, a dermatologist should be consulted. The diagnosis needs to be first carefully reviewed as patients with atopic dermatitis are at increased risk for several types of hair loss. Minoxidil, vaseline and castor oil will not help. Topical, intralesional steroids and oral immunosuppressives many need to be considered. 

If you are under the care of a doctor now, you should follow that doctor's advice. Some Doctors have found Latisse very effective in regrowing eyebrow hair.