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Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory by Francesco Maggi

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6

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)   images then there exists a constant images with the following property. If images

and there exists a constant such that ...

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