= Contact set of an obstacle problem
{title2=$\mathcal C=\{x:w(x)=f(x)\}$}
= Contact set
{synonym}
The contact set is the region where the obstacle inequality $w\geq f$ is active. On its complement the obstacle supplies no reaction; its boundary is a <free boundary problem>[free boundary], determined along with the unknown solution. A point can belong to the contact set while its contact force is zero, as for a taut horizontal string just touching an obstacle at one point. Thus equality of the gap alone does not imply strictly positive pressure.
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