On estimates of biharmonic functions on Lipschitz and convex domains

Abstract

Using Maz ’ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in ℝn. Forn ≥ 8, combinedwitharesultin[18], these estimates lead to the solvability of the Lp Dirichlet problem for the biharmonic equation on Lipschitz domains for a new range of p. In the case of convex domains, the estimates allow us to show that the Lp Dirichlet problem is uniquely solvable for any 2 − e < p < ∞ and n ≥ 4.