Weakly harmonic
From Free net encyclopedia
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.
