Weakly harmonic

In mathematics, a function <math>f<math> is weakly harmonic in a domain D if

<math>\int_D f \Delta g = 0<math>

for all <math>g<math> 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, <math>f<math> is weakly harmonic if and only if it is a harmonic function.