Periodic Homogenization of the Principal Eigenvalue of Second-Order Elliptic Operators

被引：0

作者：

Davila, Gonzalo ^{[1
]}

Rodriguez-Paredes, Andrei ^{[2
]}

Topp, Erwin ^{[3
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Ave Espana, Valparaiso 1680, Chile

[2] Univ Concepcion, Dept Matemat, Ave Esteban Iturra S-N Barrio Univ,Casilla 160 C, Concepcion, Chile

[3] Univ Santiago Chile, Dept Matemat & CC, Casilla 307, Santiago, Chile

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2023年 / 88卷 / 01期

关键词：

Second-order elliptic equations; Eigenvalue problem; Homogenization; Rate of convergence; MAXIMUM PRINCIPLE; VISCOSITY SOLUTIONS; CONVERGENCE; RATES;

D O I：

10.1007/s00245-023-09979-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：19

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