You would need to mount wooden strips along the walls that screw into the studs. Then the desktop sits on top of those strips and is fastened from the underside to the strips.
To achieve a more sleek look you could also consider the use of some lengths of aluminum angle iron that is screwed into the studs and into the bottom side of the desk surface.
Either type of mounting strip could be painted to match the wall to make it much less noticeable.
You will want to get this mounting strip along as many edges as possible and into as many studs as possible. Cantilever forces due to the open out side corner of the desk can be significant so make sure of two key things:
- Make sure that the desk top material itself can withstand the
cantilever forces without a lot of flex and breakage. (Unsupported
thin particle board would not be a good choice).
- Make sure that fasteners used up into the bottom of the desk surface
get a good bite into the material.
Here is a picture showing a cross section of the wall and desk showing how the aluminum angle stock would be applied. You would likely want to use screws into the studs that are a bit longer than what I showed.