ABSTRACT
In this paper, we study the homogenization of quasilinear elliptic problems with a jump on the interface between the two components proportional to the flux depending on a real parameter γ. The data is presumed to be an function and consequently, we consider the notion of renormalized solutions.
In the homogenization process, we employ the periodic unfolding method. The homogenized problem was afterwards identified to be a quasilinear elliptic problem with data for the case that the parameter γ is between and 1 and for the case where γ is less than .
2020 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would also like to give their thanks to the anonymous referees for their insightful comments and suggestions. The authors would like to express their deepest gratitude to the Office of the Vice President for Academic Affairs of the University of the Philippines (UP) for funding this research.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 A function is said to be Carathéodory if
the map is continuous for a.e. ;
the map is measurable for all