Definition
Regularity criterion
A specified additional condition that implies a stated regularity or continuation conclusion for a solution class.
A regularity criterion for a PDE is a theorem of the form: every solution in a specified class that satisfies an additional condition has a stated regularity property, such as being a classical solution on a region or admitting continuation beyond an endpoint. The criterion includes the equation, dimension, domain, force, solution class, and exact norm or geometric condition.
Contrapositive
If a finite norm guarantees continuation, failure of that continuation forces failure of the norm condition, provided all other hypotheses still hold. Different norms or different solution classes cannot be substituted without a theorem.