Abstract
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∂z¯3ω=ff∈CD¯ with Dirichlet boundary value conditions ωzz¯zz¯T=γ2∈CT,ωzz¯T=γ1∈CT and ωT=γ0∈Hom+T,∂Ω to be Lipschitz continuous are presented.
Highlights
Let D be the unit disk in the complex plane C and denote T zD
G(0) 0, where h and g are analytic in D and unique determined by f
By [[4], eorem 3.2.2], it is known that all solutions to equation (6) satisfying the condition (7) are given by ω(z) Pc0(z) + G1c1(z) + G2c2(z) − G3[f](z), (8)
Summary
Let D be the unit disk in the complex plane C and denote T zD. Let D and D′ be subdomains of the complex plane C. A mapping h from D onto D′ is said to be Lipschitz if there exists constant L > 0, such that the following inequality Let f ∈ Lp(D; C)(2 < p) and ω ∈ C6(D) which satisfies the following triharmonic equation: zzzz3ω f, in D, (6)
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call