= Noncontact set
{title2=$D=\{x:u(x)>g(x)\}$}
The <noncontact set> is where the unknown function is strictly above its obstacle. For <continuous functions> it is open. Every smooth variation with <compact support> in this set remains feasible with either sign when its amplitude is small enough. The <first variation> therefore vanishes there, yielding the unconstrained <Euler-Lagrange equation>. On the complementary <contact set of an obstacle problem>, only the appropriate one-sided <variational inequality> is available globally.
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