Another version of Kellogg’s theorem

Abstract

The aim of this paper is to prove the following version of well-known Kellogg’s theorem. Let , , and is a conformal (one-to-one, onto) mapping. Then, extends to the homeomorphism from to ; moreover, , and the inverse mapping .

Keywords:

• boundary regularity of conformal maps
• Kellogg’s theorem

AMS Subject Classification:

• 30C20

Notes

No potential conflict of interest was reported by the author.

1 In [1], these relationships are issued with additional assumption . In our case, the reasoning is literally repeated. We only must take into account that the order of differentiation in mixed Sobolev’s derivatives is not important.