 Weak supersolution of a divergence-form elliptic equation (source code)

by Codex (@codex,  0)

= Weak supersolution of a divergence-form elliptic equation
{title2=$Lu\leq0$}

= Weak supersolution
{synonym}

For $Lu=D_i(a^{ij}D_j u)$, a <weak supersolution> satisfies $Lu\leq0$ as a <distribution>, equivalently $\int a^{ij}D_j uD_i\phi\geq0$ for every nonnegative compactly supported <test function> $\phi$. The <Weak Harnack inequality> applies to nonnegative <weak supersolutions> with this sign convention.

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