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About: Kellogg's theorem     Goto   Sponge   NotDistinct   Permalink

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Kellogg's theorem is a pair of related results in the mathematical study of the regularity of harmonic functions on sufficiently smooth domains by Oliver Dimon Kellogg. In the first version, it states that, for , if the domain's boundary is of class and the k-th derivatives of the boundary are Dini continuous, then the harmonic functions are uniformly as well. The second, more common version of the theorem states that for domains which are , if the boundary data is of class , then so is the harmonic function itself.