论文标题
与Hölder系数的免费接口问题的规律性结果
Regularity Results for a free interface problem with Hölder coefficients
论文作者
论文摘要
我们研究一类涉及大量和界面能量的变分问题。大量能量是Dirichlet类型的，尽管具有非常通用的形式，允许未知变量$ u $和位置$ x $的依赖性。我们采用$λ$ -Minimizers的规律性理论来研究自由接口的规律性。该论文的标志是关于系数相对于$ x $和$ u $的依赖性的温和规律性假设。
We study a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type albeit of very general form allowing the dependence from the unknown variable $u$ and the position $x$. We employ the regularity theory of $Λ$-minimizers to study the regularity of the free interface. The hallmark of the paper is the mild regularity assumption concerning the dependence of the coefficients with respect to $x$ and $u$ that is of Hölder type.
