Corrector problem in the deterministic homogenization of nonlinear elliptic equations

ABSTRACT

We carry out the deterministic homogenization of nonlinear elliptic operators beyond periodicity. To proceed with, we prove the existence of nonlinear correctors in the usual distributional sense. This lays the foundation for the study of regularity results in the nonlinear deterministic homogenization theory beyond the periodic setting.

KEYWORDS:

• Corrector problem
• deterministic homogenization
• approximation

AMS SUBJECT CLASSIFICATIONS:

• 35B40
• 46J10

Acknowledgements

The work of J.L.W. was supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM); he also acknowledges the support of the Alexander von Humboldt Foundation. G.C. is a member of GNAMPA of INDAM.

Notes

No potential conflict of interest was reported by the authors.

This paper is dedicated to the memory of V. V. Zhikov.

Additional information

Funding

This was supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM); Alexander von Humboldt Foundation.