Antiperspirant - the likes of Sure Maximum Protection is sold in most stores which can help prevent sweating more than standard antiperspirants, or there are products like Odaban and Perspi-Guard which are more effective (apply at night, they prevent sweating in the area, over time you need to use them less often). If bad talk to your doctor about what's available on prescription.
Powder - not always fantastic as the powder absorbs the sweat and can make a mess, but sometimes it's useful to use sparingly along with antiperspirant, and if you use a scented powder like the types you can get from Lush then it helps you smell nice too.
Pantiliners - pop in your bra, they aren't ideal but something like this or wearing a light vest top under your normal clothing can help to absorb sweat so to avoid sweat showing on clothing or if you have something like a date you can wear these beforehand then go remove (when they're sweaty and gross) just beforehand so at least you're a bit fresher for your date, you know?
10 Tips On How To Deal With Boob Sweat This Summer -
http://www.gurl.com/2015/06/17/tips-on-how-to-deal-with-stop-breast-boob-sweat-this-summer/#ixzz4kadTGMOI