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Theme for TIFR Centre For Applicable Mathematics, Bangalore

Abstract: In this talk, we will discuss the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The homogeneous Neumann condition is prescribed on the oscillating part of the boundary, and the Dirichlet condition on a separate part. We will explain the homogenization results in the sense of weak $$L^2$$ convergence of the solutions and their flows, under natural hypothesis on the regularity of the domain using unfolding operators.