This code adapted from http://mathematica.stackexchange.com/questions/14863/placing-a-contourplot-under-a-plot3d works prety well.

    u[x_, y_] := x^.5 y^.5
    contour = 
     ContourPlot[u[x, y], {x, 0, 1}, {y, 0, 1}, PlotRange -> {0, 1}, 
      Axes -> False, Contours -> 15, PlotPoints -> 50, 
      PlotRangePadding -> 0, ColorFunction -> "Aquamarine"]
    potential1 = 
     Plot3D[u[x, y], {x, 0, 1}, {y, 0, 1}, PlotRange -> {0, 1}, 
      ClippingStyle -> None, MeshFunctions -> {#3 &}, Mesh -> 15, 
      MeshStyle -> Opacity[.5], 
      MeshShading -> {{Opacity[.3], Blue}, {Opacity[.8], LightBlue}}, 
      PlotRange -> {Automatic, Automatic, {min, 2}}, Lighting -> "Neutral"]
    Show[potential1, 
     Graphics3D[contour[[1]] /. {x_Real, y_Real} :> {x, y, 0}], 
     BoxRatios -> {1, 1, 0.6}, FaceGrids -> {Back, Left}]


Here is the outcome

[![enter image description here][1]][1]

I wonder how
 reuse the color function on the contour plot to have identical colors

  [1]: https://i.sstatic.net/vdgM9.png