Polyharmonic equations involving surface measures

2022/12/13 by Müller, Marius · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.06624

Abstract

This article studies (optimal) W^2m-1,∞-regularity for the polyharmonic equation (-Δ)^m u = Q H^n-1 \llcorner Γ, where Γ is a (suitably regular) (n-1)-dimensional submanifold of ℝⁿ, H^n-1 is the Hausdorff measure, and Q is some suitably regular density. We extend findings in [9], where the second-order equation -div(A(x)∇ u) = Q H^n-1 \llcorner Γ is studied. As an application we derive (optimal) W^3,∞-regularity for solutions of the biharmonic Alt-Caffarelli problem in two dimensions.

Cited by

• An anisotropic Alt-Caffarelli problem of higher order

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