Continuously differentiable in the context of Harmonic function

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function ${\displaystyle f\colon U\to \mathbb {R} ,}$ where U is an open subset of ⁠${\displaystyle \mathbb {R} ^{n},}$⁠ that satisfies Laplace's equation, that is,$${\displaystyle {\frac {\partial ^{2}f}{\partial x_{1}^{2}}}+{\frac {\partial ^{2}f}{\partial x_{2}^{2}}}+\cdots +{\frac {\partial ^{2}f}{\partial x_{n}^{2}}}=0}$$everywhere on U. This is usually written as$${\displaystyle \nabla ^{2}f=0}$$or$${\displaystyle \Delta f=0}$$