The Dirichlet problem for the biharmonic equation in a Lipschitz domain
Björn E. J. Dahlberg, Carlos E. Kenig, Gregory C. Verchota · Annales de l’institut Fourier · 1986
In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator Δ 2 , on an arbitrary bounded Lipschitz domain D in R n . We establish existence and uniqueness results when the boundary values have first derivatives in L 2 ( ∂ D ) , and the normal derivative is in L 2 ( ∂ D ) . The resulting solution u takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of ∇ u is shown to be in L 2 ( ∂ D ) .