Interior Imperfect Ignition Cannot Occur on a Set of Positive Measure

Abstract.

For the differential inequality $u_{t}-\Delta u \geq 0$, it is proved that the dead core of the solution $D=\bigcup_{0\leq t \leq T}D(t) \times \{ t \}$ with $D(t)=\overline{\left\{ x\in\Omega \mid u(x,t)=+\infty\right\}}$ cannot be enclosed inside a bounded domain with positive Lebesgue measure.