Weakly harmonic function

In mathematics, a function $f$ is weakly harmonic in a domain D if

$\int _{D}f\Delta g=0$

for all $g$ with compact support in D and continuous second derivatives, where Δ is the Laplacian. Surprisingly, this definition is equivalent to the seemingly stronger definition. That is, $f$ is weakly harmonic if and only if it is a harmonic function.