Superharmonic function
= Superharmonic function
A locally integrable real function is superharmonic in the distributional sense if its <Laplacian> is nonpositive on every nonnegative <test function>. Equivalently its negative is a <subharmonic function>. The canonical lower semicontinuous representative satisfies the reverse ball mean inequality. A function both subharmonic and superharmonic has zero distributional Laplacian and a smooth <harmonic function> representative by the <Weyl lemma>.