论文标题
二阶椭圆算子的主要特征值的定期均质化
Periodic homogenization of the principal eigenvalue of second-order elliptic operators
论文作者
论文摘要
在本文中，我们调查了主要特征值问题的同质化结果，该问题与$ 1 $均匀，均匀的椭圆形，二阶操作员有关。在相当普遍的假设下，我们证明了与振荡操作员相关的主要特征Pair将与有效的操作员相关的本征与特征。这包括完全非线性操作员的情况。在额外的规律性/凸度假设下，为线性和非线性问题提供了特征值的收敛速率。最后，对于线性问题，获得了适当归一化的本征函数的线性收敛速率（根据振荡参数）。
In this paper we investigate homogenization results for the principal eigenvalue problem associated to $1$-homogeneous, uniformly elliptic, second-order operators. Under rather general assumptions, we prove that the principal eigenpair associated to an oscillatory operator converges to the eigenpair associated to the effective one. This includes the case of fully nonlinear operators. Rates of convergence for the eigenvalues are provided for linear and nonlinear problems, under extra regularity/convexity assumptions. Finally, a linear rate of convergence (in terms of the oscillation parameter) of suitably normalized eigenfunctions is obtained for linear problems.
