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You could stand them down and then repaint them. If you use a chalk paint, you just have to sand down the worst of it, clean it, and then paint it. Chalk paint can self level and it's easy to work with.
Hello
I had a white cabinet that I just needed to use a warm iron and the white finish was reapplied along the edges.
Alternatively at another home with white cabinets I was able to disguise defects using an appliance repair paint. I have found this white Rustoleum paint to be excellent for touchup! It was a few dollars at Walmart and I use it on cabinets my freezer and so much more. Its very thick and in a nail polish type dispenser.
On Amazon it’s available in black and white.
https://www.amazon.com/Rust-Oleum-213174-6-Ounce-Specialty-Appliance/dp/B000RNPGKO/ref=pd_sim_328_1?_encoding=UTF8&pd_rd_i=B000RNPGKE&pd_rd_r=c321c116-82e9-11e8-aafc-3933c5359799&pd_rd_w=7tICF&pd_rd_wg=Yoz0s&pf_rd_i=desktop-dp-sims&pf_rd_m=ATVPDKIKX0DER&pf_rd_p=7967298517161621930&pf_rd_r=WMXFVAMD287DX43W8WKR&pf_rd_s=desktop-dp-sims&pf_rd_t=40701&refRID=WMXFVAMD287DX43W8WKR&th=1
Hi Lar, you can lightly sand them and paint with chalk paint, it will give you a chance to change them to a color you like as well.
https://www.youtube.com/watch?v=HeIT8gTwAP8
not knowing how the white finish was applied or what it is (paint or Formica) it is hard to advise. If paint, sand down the area and repaint or repaint all the cabinets with epoxy paint. If Formica, call a cabinate maker and ask his advice, if a very small area try reapplying with a glue filled syringe to get under the Formica or try ironing it back on with a warm iron.