What can we do about laminate peeling near the oven heat?

MBF or Particle board isn't 'real' wood, even though made from wood byproducts ... can you contact the manufacturer for suggestions? Color is fixable -- paint is your friend!

Terry, intense heat might always make any laminate peel. I can't see the door clearly but would purchasing a wood door help? You can buy wood doors online. Use wood for the cabinets near the oven and mdf for the uppers. For the color, use a good quality paint, paint all of the cabinets and it will all match up in the end. Usually when laminate peels, you can use an iron and the glue will heat up and melt it back on. However; in this case it seems to be the heat of the oven that's an issue so that might not work.

If your door has a straight edge (not tapered), you can buy a piece of aluminum angle, cut it to the size of your door, and attach it to the edge with screws.

Maybe consider checking the door seal on the oven? There's obviously a load of heat coming out there & that cannot be good for your bills or your cooking

This looks like a thermofoil covering on your door, which is basically plastic and cannot be fixed .. It melts. That is definitely not laminate as it cannot be bent around a profile like that (retired cabinetmaker here) You can peel the thermofoil off of the door and paint it as it is MDF underneath. Other than that you would need to replace it. Thermofoil is a great product but cannot withstand extreme heat. If you cannot put your hand there and it is too hot....it is too hot for these doors.

Pmacdermid is right. It is Thermofoil. Installed a lot of those in my day. They were low cost and looked great.Peeling it off. sanding the MDF, and painting is the only solution. Kind of surprised a cabinet is so close to the range. Usually they install a spacer board between the range and cabinet.