Home > Partial Differential Equations > Weakly harmonic implies harmonic

Weakly harmonic implies harmonic


Suppose u \in C^0(\Omega) is weakly harmonic on an open set \Omega, i.e. the relation \displaystyle \int_\Omega u \Delta \phi dx =0 holds for all \phi \in C_0^2(\Omega). Show that u is harmonic in \Omega.

PHD Iowa (6202)

See this blog post for a proof.

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