If you want to do the mesh lines and other details, you can use more options. These make no sense to the plot because I just made things up and copied the MeshFunction from an example in the documentation to show you.

DensityPlot[Sin[x + Cos[y]], {x, y} \[Element] Disk[{0, 0}, {6, 3}], 
 AspectRatio -> Automatic, BoundaryStyle -> Directive[Red, Thick], 
 Frame -> None, Mesh -> 10, 
 MeshFunctions -> {Re[Sqrt[#1 + I #2]] &, Im[Sqrt[#1 + I #2]] &}]

gives

By the way, I with I knew why

ContourPlot[x, Element[{x, y}, Disk[]]]
Plot3D[x, Element[{x, y}, Disk[]]]

draw the plot on a disk, but the following does not:

ParametricPlot3D[{x, y, x}, Element[{x, y}, Disk[]]]

Actually, it did up to version 12.0. But then that capability was inexplicably removed.

Gianluca,

This works:

ParametricPlot3D[{x, y, x}, Element[{x, y}, Disk[]], 
 RegionFunction -> Function[{x, y, z}, x^2 + y^2 < 1]]

or better yet,

ParametricPlot3D[{x, y, x}, Element[{x, y}, Disk[]], 
 RegionFunction -> Function[{x, y, z}, Element[{x, y}, Disk[]]]]

but you should report that the element syntax no longer automatically limits the region.

Regards

Neil

Thank you sir! This way can help me solve this problem greatly!

Regards

Tony