Polyharmonic equations involving surface measures.

This article studies (optimal) W2m-1,∞-regularity for the polyharmonic equation (-Δ)mu = Q Hn-1 ... Γ, where Γ is a (suitably regular) (n - 1)-dimensional submanifold of ℝn, Hn-1 is the Hausdorff measure, and Q is some suitably regular density. As an application, we derive (optimal) W3, ∞-regularity for solutions of the biharmonic Alt-Caffarelli problem in two dimensions. [ABSTRACT FROM AUTHOR]