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Locally periodic homogenization. (English) Zbl 1064.35017

Summary: Two linear second-order (an elliptic bvp and parabolic ivp) PDEs are homogenized. The coefficients are supposed to be locally periodic, Lipschitz and bounded. Compared to a previous work of the authors [Lect. Notes Math. 1857, 363–392 (2005; Zbl 1067.35009)], they provide a new and simpler proof and weaken the hypotheses of the main theorem. Both probabilistic and analytic arguments are used.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J25 Boundary value problems for second-order elliptic equations
35K15 Initial value problems for second-order parabolic equations

Citations:

Zbl 1067.35009
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