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This is a Quantitative Study study.

October 9, 2025Open Access

Quantitative homogenisation for differential equations with highly anisotropic partially degenerating coefficients

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This analysis reveals asymptotic behaviour of the resolvent in composite media, indicating challenges in ellipticity loss.

The study describes the asymptotic behaviour of the resolvent for anisotropic differential operators in composite media.
As the period approaches zero, ellipticity is lost in certain directions, complicating the analysis of the system.
A new boundary layer analysis is introduced to account for directional dependence and error estimates in the operator.
This work builds on previous results in the field while addressing unique challenges posed by the high-contrast scaling.

Cooper et al. (2025) studied this question.

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