A cubic inequality for triangle sides

This inequality states that for non-negative reals $a, b, c$ and $t > 0$, $a^t(a-b)(a-c) + b^t(b-a)(b-c) + c^t(c-a)(c-b) \ge 0$. It is a favorite tool in olympiad problems and is named after a German mathematician known for his work in representation theory.