Weakly harmonic function

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.

ee also

* Weak solution
* Weyl's lemma


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