This file (download) contains a construction of a nowhere convex, non-negative, strictly increasing, continuously differentiable function tightly bounded from above by a convex one. It also contains a motivation to consider such an object.

This example was presented during:

• the exercise classes to Aspects of Nonlinear Wave Equations (summer semester 2016, Karlsruhe),
• the talk O pewnej funkcji nigdzie wypukłej z wypukłym ograniczeniem górnym (in Polish) [About a certain nowhere convex function with a convex upper bound] (Katowice, 21.12.2016).