Assuming H-convergence of the diffusion tensors, for small homogenization parameters there exists exactly one weak solution close to a given non-degenerate weak solution of the homogenized semilinear elliptic system.
Gr¨ oger, AW1,p-estimate for solutions to mixed boundary value problems for second-order elliptic differential equations
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An H-convergence-based implicit function theorem for homogenization of nonlinear non-smooth elliptic systems
Assuming H-convergence of the diffusion tensors, for small homogenization parameters there exists exactly one weak solution close to a given non-degenerate weak solution of the homogenized semilinear elliptic system.