Limiting tests and the rate theorem

The representatives converge before taking equation classes. No quotient cancellation is needed to rescue a divergent representative family.

X-B's crude bound differentiated the ramp before integrating the solution and consequently contained powers of ${\epsilon }^{-1}$. Lemma lem:flux explains why that bound does not describe the present fixed-input limit: ${\partial }_{t}u+F$ is estimated without differentiating $F$. The theorem supplies boundedness and the actual rate on the declared supports.