A wall-mounted desk can be represented as a simply supported structured cantilever beam. I've analyzed this system (depicted below) under two loading conditions. The first is a point load placed at the end of the desk that represents the max stress state. This represents the case where a user leans or even perhaps sits on the edge of the desk. The second condition, a uniform distributed load, models the a desk with more normal loading (books, computers, etc.).
The image above also shows the free body diagrams for the desktop and the wall mount under both loading conditions.
The two parameters evaluated in this analysis were maximum stress locations and deflection at the end of the desktop. A first order analysis allows the analysis to be broken down into three distinct deflection types via superposition:
Axial Loading: along the upper half of the vertical support structure
Bending: along the full length of the vertical support
Cantilever Bending: Along the length of the desktop
A qualitative view of these loading conditions applied to our wall-mount desk shows two points of elevated stress during loading. These are depicted as A and B below. Point A is caused by a combination of axial loading and bending in the vertical beam. Point B is caused by the cantilever bending.
Lastly,the deflection of the desktop can be approximated by the analysis below: