论文标题
涉及表面测量的多谐和方程
Polyharmonic equations involving surface measures
论文作者
论文摘要
本文研究（最佳）$ w^{2m-1，\ infty} $ - polyharmonic方程$（ - δ）^m u = q \; \mathcal{H}^{n-1} \llcorner Γ$, where $Γ$ is a (suitably regular) $(n-1)$-dimensional submanifold of $\mathbb{R}^n$, $\mathcal{H}^{n-1}$ is the Hausdorff measure, and $Q$ is some suitably regular density.我们在[9]中扩展了发现，其中二阶方程$ - \ mathrm {div}（a（x）\ nabla u）= q \; \ Mathcal {h}^{n-1} \llcornerγ$。作为一个应用程序，我们得出（最佳）$ w^{3，\ infty} $ - 在两个维度上的Biharmonic Alt-Caffarelli问题解决方案的规律性。
This article studies (optimal) $W^{2m-1,\infty}$-regularity for the polyharmonic equation $(-Δ)^m u = Q \; \mathcal{H}^{n-1} \llcorner Γ$, where $Γ$ is a (suitably regular) $(n-1)$-dimensional submanifold of $\mathbb{R}^n$, $\mathcal{H}^{n-1}$ is the Hausdorff measure, and $Q$ is some suitably regular density. We extend findings in [9], where the second-order equation $-\mathrm{div}(A(x)\nabla u) = Q \; \mathcal{H}^{n-1} \llcorner Γ$ is studied. As an application we derive (optimal) $W^{3,\infty}$-regularity for solutions of the biharmonic Alt-Caffarelli problem in two dimensions.
