Homogenization of elliptic systems with Neumann boundary conditions

Kenig, Carlos¹ ; Lin, Fanghua² ; Shen, Zhongwei³

¹ Department of Mathematics, University of Chicago, Chicago, Illinois 60637
² Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
³ Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506

Journal of the American Mathematical Society, Tome 26 (2013) no. 4, pp. 901-937

Résumé

For a family of second-order elliptic systems with rapidly oscillating periodic coefficients in a $C^{1,\alpha }$ domain, we establish uniform $W^{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates on solutions with Neumann boundary conditions.

Détail

DOI : 10.1090/S0894-0347-2013-00769-9

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