Talk:Weakly harmonic function

The harmonic function article summary states:

There also exists a seemingly weaker definition that is equivalent. Indeed a function is harmonic if and only if it is weakly harmonic.

But the weakly harmonic function article states:

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.

--Marcianx (talk) 23:31, 13 April 2008 (UTC)

You're right, something is wrong here. In the MIT opencourseware

http://ocw.mit.edu/OcwWeb/Mathematics/18-156Spring2004/LectureNotes/

there are some lecture notes on weakly harmonic functions. Although it "looks" like weakly harmonic functions do not need to be twice continuously differentiable, it turns out that they are, and the two are equivalent. I will edit this article accordingly. --Paul Laroque (talk) 02:04, 13 April 2009 (UTC)

Unclear statement

It is unclear what this statement is saying:

" In this case, we have the somewhat surprising result that a function is weakly harmonic if and only if it is harmonic"

because it is entirely unclear what "in this case" means here. 2601:204:F181:9410:2E:DFAF:B4BF:159 (talk) 16:38, 16 June 2025 (UTC)