Lipschitz Continuity for the Solutions of Triharmonic Equation

摘要

Let D be the unit disk in the complex plane C and denote T=?D. Write Hom+T,?Ω for the class of all sense-preserving homeomorphism of T onto the boundary of a C2 convex Jordan domain Ω. In this paper, five equivalent conditions for the solutions of triharmonic equations ?z?zˉ3ω=ff∈CDˉ with Dirichlet boundary value conditions ωzzˉzzˉT=γ2∈CT,ωzzˉT=γ1∈CT and ωT=γ0∈Hom+T,?Ω to be Lipschitz continuous are presented.