1 Answers
In mathematics, a function f {\displaystyle f} is weakly harmonic in a domain D {\displaystyle D} if
for all g {\displaystyle g} with compact support in D {\displaystyle D} and continuous second derivatives, where Δ is the Laplacian. This is the same notion as a weak derivative, however, a function can have a weak derivative and not be differentiable. In this case, we have the somewhat surprising result that a function is weakly harmonic if and only if it is harmonic. Thus weakly harmonic is actually equivalent to the seemingly stronger harmonic condition.
4 views
Answered