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- Kellogg's_theorem abstract "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.Kellogg's method of proof analyzes the representation of harmonic functions provided by the Poisson kernel, applied to an interior tangent sphere. In modern presentations, Kellogg's theorem is usually covered as a specific case of the boundary Schauder estimates for elliptic partial differential equations.".
- Kellogg's_theorem wikiPageID "38616928".
- Kellogg's_theorem wikiPageRevisionID "540342485".
- Kellogg's_theorem hasPhotoCollection Kellogg's_theorem.
- Kellogg's_theorem subject Category:Harmonic_functions.
- Kellogg's_theorem subject Category:Potential_theory.
- Kellogg's_theorem comment "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.".
- Kellogg's_theorem label "Kellogg's theorem".
- Kellogg's_theorem sameAs m.0r8qbxc.
- Kellogg's_theorem sameAs Q6385835.
- Kellogg's_theorem sameAs Q6385835.
- Kellogg's_theorem wasDerivedFrom Kellogg's_theorem?oldid=540342485.
- Kellogg's_theorem isPrimaryTopicOf Kellogg's_theorem.