论文标题
退化Alt-Caffarelli功能的牙尖不存在
Non-existence of cusps for degenerate Alt-Caffarelli functionals
论文作者
论文摘要
我们消除了Alt-caffarelli功能$ j_ {q}（v，ω）的\ textit {demenerate} \ textit {demenerate}的cusps的存在：= \int_Ω| \ nabla v |^2 + q^2 + q^2 + q^2 + q^2（x）x（x）χ_ { \ text {dist}（x，γ）^γ$ for $γ$ a aptine $ k $ - 平面和$ 0 <γ$。这个问题的启发是由Arama和Leoni对Stokes Wave的变异表述的概括。消除尖尖意味着[McCurdy20]的结果实际上描述了整个自由界面，因为它与$γ$相交。
We eliminate the existence of cusps in a class of \textit{degenerate} free-boundary problems for the Alt-Caffarelli functional $J_{Q}(v, Ω):= \int_Ω|\nabla v|^2 + Q^2(x)χ_{\{v>0\}}dx,$ so-called because $Q(x) = \text{dist}(x, Γ)^γ$ for $Γ$ an affine $k$-plane and $0< γ$. This problem is inspired by a generalization of the variational formulation of the Stokes Wave by Arama and Leoni. The elimination of cusps implies that the results of [Mccurdy20] in fact describe the entire free-boundary as it intersects $Γ$.
