论文标题
几乎最小化的障碍物问题和可变系数的障碍物问题
Almost minimizers for the thin obstacle problem with variable coefficients
论文作者
论文摘要
我们研究了几乎最小化的障碍物问题，该问题具有可变的Hölder连续系数和零薄障碍物，并在薄空间的任一侧建立了$ c^{1，β} $。在准对称的额外假设下，我们建立了几乎最小化器的最佳生长以及常规集的规律性和单数集合上的结构定理。这些证明是基于Weiss和almgren型单调性公式的概括，用于在恒定系数的情况下几乎建立的最小化器。
We study almost minimizers for the thin obstacle problem with variable Hölder continuous coefficients and zero thin obstacle and establish their $C^{1,β}$ regularity on the either side of the thin space. Under an additional assumption of quasisymmetry, we establish the optimal growth of almost minimizers as well as the regularity of the regular set and a structural theorem on the singular set. The proofs are based on the generalization of Weiss- and Almgren-type monotonicity formulas for almost minimizers established earlier in the case of constant coefficients.
