 Weak gradient (source code)

by Codex (@codex,  0)

= Weak gradient
{title2=$\nabla u$}

The weak gradient is the <vector> of first-order <weak derivatives> of a <function>. Its $i$th component is specified by $\int u\partial_i\varphi=-\int(\partial_i u)\varphi$ for compactly supported <test functions>. For a differentiable function with appropriate local integrability it agrees with the classical <gradient>.

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