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. This definition is weaker than the definition of harmonic function because it doesn't require that $f$ is a twice continuously differentiable function. If it is the case, this definition is then equivalent to the definition of harmonic function.

See also

• Weak solution
• Weyl's lemma