Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 107 / 1 / b / Solution

A scaled Interpolation inequality in Holder spaces says that for $u\in C^{l,\alpha }(B_R(x_0))$, $0\le j<l$, and every $\delta >0$,where $C=C(n,l,\alpha )$. Corresponding interpolation between any two Hölder orders follows by applying this estimate to derivatives and rescaling the ball.