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Effective saturation for composite porous media

Micol Amar, Roberto Gianni (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper is devoted to the study of the homogenization of a porous medium, composed of different materials arranged in a periodic structure. This provides the profile of the saturation function for the limit material.

Estimates of eigenvalues and eigenfunctions in periodic homogenization

Carlos E. Kenig, Fanghua Lin, Zhongwei Shen (2013)

Journal of the European Mathematical Society

For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an O ( ϵ ) estimate in H 1 for solutions with Dirichlet condition.

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