A property of $C^{k,\alpha }$ functions

Robert Dalmasso

Let $f$ be a nonnegative function of class $C^k$ ($k\ge 2$) such that $f^{(k)}$ is H\''older continuous with exponent $\alpha$ in $(0,1]$. If $f^{\prime }(x)=\cdots =f^{(k)}(x)=0$ when $f…