@article{Donato2023, 
author = {Patrizia Donato and Olivier Guibé and Alip Oropeza},
title = {Corrector results for a class of elliptic problems with nonlinear Robin conditions and        L    1   data},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {3},
pages = {1236-1259},
keywords = {homogenization, periodic unfolding, nonlinear Robin condition, correctors, renormalized solutions, integrable data},
url = {https://www.sciopen.com/article/10.3934/nhm.2023054},
doi = {10.3934/nhm.2023054},
abstract = {In this paper, we consider a class of elliptic problems in a periodically perforated domain with        L    1   data and nonlinear Robin conditions on the boundary of the holes. Using the framework of renormalized solutions, which is well adapted to this situation, we show a convergence result for the truncated energy in the quasilinear case. When the operator is linear, we also prove a corrector result. Since we cannot expect to have solutions belonging to        H    1  , the main difficulty is to express the corrector result through the truncations of the solutions, together with the fact that the definition of a renormalized solution contains test functions which are nonlinear functions of the solution itself.}
}