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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  ε . The generalized Sobolev space is constructed, and the epiconvergence method is considered to find the limit problem with interface conditions.

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