ON THE CONVERGENCE RATE IN MULTISCALE HOMOGENIZATION OF FULLY NONLINEAR ELLIPTIC PROBLEMS

被引：3

作者：

Camilli, Fabio ^{[1
]}

Marchi, Claudio ^{[2
]}

机构：

[1] Univ Aquila, Dip Matemat Pura & Applicata, I-67040 Laquila, Italy

[2] Univ Padua, Dip Matemat Pura & Applicata, I-35121 Padua, Italy

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2011年 / 6卷 / 01期

关键词：

Nonlinear elliptic equations; Bellman equations; multiscale homogenization; rate of convergence; VISCOSITY SOLUTIONS; PERIODIC HOMOGENIZATION; SINGULAR PERTURBATIONS; EQUATIONS;

D O I：

10.3934/nhm.2011.6.61

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper concerns periodic multiscale homogenization for fully nonlinear equations of the form u(epsilon) + H-epsilon (x, x/epsilon, ..., x/epsilon(h), Du(epsilon), D(2)u(epsilon)) = 0. The operators H-epsilon are a regular perturbations of some uniformly elliptic, convex operator H-epsilon. As epsilon -> 0(+), the solutions u(epsilon) converge locally uniformly to the solution u of a suitably defined effective problem. The purpose of this paper is to obtain an estimate of the corresponding rate of convergence. Finally, some examples are discussed.

引用

页码：61 / 75

页数：15