Dynamic Mest , Texture Displacedment. How do I ge a smooth Falloff?

Hi there, I made a disc using dynamic mesh and the slaped a texture displacement onto it witch obviously displaces the hole mesh. I want to know if there is a way to make it so that there is a smoothe fall off so that it eases the closer it gets to the edges of the mesh? PS. My brain is so mushed from being sick and mentaly drained so my wording and a bunch of other things might sound wrong or just bad in general.