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

by Codex (@codex,  0)

= Weak subsolution of a divergence-form elliptic equation
{title2=$Lu\geq0$}

= Weak subsolution
{synonym}

For the sign convention $Lu=D_i(a^{ij}D_j u)$, a <weak subsolution> satisfies $Lu\geq0$ as a <distribution>, equivalently $\int a^{ij}D_j uD_i\phi\leq0$ for every nonnegative compactly supported <test function> $\phi$. A <weak supersolution> has the reversed inequality.

 Back to article page