On Weak Solvability of Boundary Value Problem with Variable Exponent Arising in Nanostructure

This work is devoted to study the limit behavior of weak solutions of an elliptic problem with variable exponent, in a containing structure, of an oscillating nanolayer of thickness and periodicity parameter depending on epsilon. The generalized Sobolev space is constructed, and the epiconvergence method is considered to find the limit problem with interface conditions.

Automated summary

This study focuses on the limit behavior of weak solutions of an elliptic problem with variable exponent in a specific structure, involving an oscillating nanolayer with thickness and periodicity parameters depending on epsilon. A generalized Sobolev space is constructed, and the epiconvergence method is used to determine the limit problem with interface conditions.