Hölder continuity of harmonic quasiconformal mappings

: Arsenović M., Manojlović V., Vuorinen M.

: 2011

: Journal of Inequalities and Applications

: 2011

: 37

: 5

: 1025-5834

DOI: https://doi.org/10.1186/1029-242X-2011-37

: http://api.elsevier.com/content/abstract/scopus_id:84868123182

We prove that for harmonic quasiconformal mappings α-Hölder continuity on the boundary implies α-Hölder continuity of the map itself. Our result holds for the class of uniformly perfect bounded domains, in fact we can allow that a portion of the boundary is thin in the sense of capacity. The problem for general bounded domains remains open. © 2011 Arsenoviéć et al; licensee Springer.