Hölder continuity of harmonic quasiconformal mappings
: Arsenović M, Manojlović V, Vuorinen M
Publisher: SPRINGER INTERNATIONAL PUBLISHING AG
: 2011
: Journal of Inequalities and Applications
: Journal of Inequalities and Applications
: J INEQUAL APPL
: 37
: 2011
: 37
: 5
: 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.