标题： 诺伊曼到斯捷克洛夫特征值：渐近和单调性结果 显示英文标题

标题： Neumann to Steklov eigenvalues: asymptotic and monotonicity results

摘要： 我们考虑拉普拉斯算子的Steklov特征值作为在球体边界质量集中问题中的极限Neumann特征值。我们讨论Neumann特征值的渐近行为，并找到其在极限问题中的导数的显式公式。我们推导出Neumann特征值在极限情况下具有单调行为，并且Steklov特征值局部最小化Neumann特征值。 显示英文摘要

摘要： We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of mass concentration at the boundary of a ball. We discuss the asymptotic behavior of the Neumann eigenvalues and find explicit formulas for their derivatives at the limiting problem. We deduce that the Neumann eigenvalues have a monotone behavior in the limit and that Steklov eigenvalues locally minimize the Neumann eigenvalues.