Two further applications of differentiation theory
6.1 Campanato's criterion
Campanato's criterion is a cornerstone in the regularity theory for variational problems, as it characterizes Hölder continuity in terms of the uniform decay of certain integral averages. We shall use this criterion in Section 26.2.
Theorem 6.1 (Campanato's criterion) then there exists a constant with the following property. If
and there exists a constant such that ...