论文标题
可变系数的罚款薄障碍问题的存在和规律性结果
Existence and regularity results for the penalized thin obstacle problem with variable coefficients
论文作者
论文摘要
在本文中，我们对椭圆形算子形成的两质量边界障碍物问题进行了全面处理，该问题是由对流体动力学和热液应用的应用。具体而言，我们证明了解决方案的存在，独特性和最佳规律性，并建立了自由边界的结构特性。这些证明是基于Almgren，Weiss和Monneau-Type的量身定制的单调性公式，并结合了经典的倾斜导数问题理论。
In this paper we give a comprehensive treatment of a two-penalty boundary obstacle problem for a divergence form elliptic operator, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and optimal regularity of solutions, and establish structural properties of the free boundary. The proofs are based on tailor-made monotonicity formulas of Almgren, Weiss, and Monneau-type, combined with the classical theory of oblique derivative problems.
