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          | Abstract: |  
          | We are concerned with periodic strongly oscillating variable exponent problems involving Leray-Lions type operators.  We first show that the problem under study is uniquely solvable and we establish  \emph{a priori} estimates. Using  a suitable convergence setting, we then provide  the homogenization result. This talk is based on a joint work with Renata Bunoiu and Claudia Timofte. |  |