How can I repair white laminate cabinets where the edges are peeling?

Rosie
by Rosie

The overall look of my white cabinets looks good. Still shiny and no stains. But on the drawers and cabinets that are used the most the edges )not the fronts_ are cracked and slightly peeling. I would like to fix them before they get worse and go down the fronts! Any ideas of a glue or repair that would be effective?

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