论文标题
自由边界和固定边界的切向接触，用于自由传输问题的变性解决方案
Tangential contact of free boundaries and the fixed boundary for variational solutions to a free transmission Problem
论文作者
论文摘要
在本文中，我们研究以下类型$$ \int_Ω\ big（\ langle a（x，x，u）\ nabla u，\ nabla u \ rangle+λ（x，x，x，u）\ big）\，dx $对于某些椭圆形和有限的矩阵$ a _ {\ pm} $，带有Hölder连续条目，以及$λ（x，x，u）=λ_ +（x）χ_{ 0 \}} $。我们证明，上述功能的最小化器的自由边界以切线方式触摸固定边界$ \部分ω$，提供边界数据的图表可平稳触及其零。此假设反映在\ eqref {dpt}条件中。
In this article we study functionals of the following type $$ \int_Ω \Big ( \langle A(x,u)\nabla u, \nabla u\rangle + Λ(x,u) \Big )\,dx $$ here $A(x,u)= A_+(x)χ_{\{u>0\}}+A_-(x) χ_{\{u\leq 0\}}$ for some elliptic and bounded matrices $A_{\pm}$ with Hölder continuous entries and $Λ(x,u) = λ_+(x) χ_{\{u>0\}} + λ_-(x) χ_{\{u\le 0\}}$. We prove that the free boundaries of minimizers of the above functional touches the fixed boundary $\partial Ω$ in a tangential fashion, provide the graph of boundary data touches its zeros smoothly. This assumption is reflected in the \eqref{DPT} condition.
