Homogenization theory of elliptic system with lower order terms for dimension two
نویسندگان
چکیده
In this paper, we consider the homogenization problem for generalized elliptic systems$ \mathcal{L}_{ \varepsilon} = -\operatorname{div}[A(x/ \varepsilon)\nabla+V(x/ \varepsilon)]+B(x/ \varepsilon)\nabla+c(x/ \varepsilon)+\lambda I $with dimension two. Precisely, will establish $ W^{1, p} estimates, Hölder Lipschitz estimates and L^p convergence results with The operator has been studied by Qiang Xu d\geq 3 in [22,23] case d 2 is remained unsolved. As a byproduct, construct Green functions their rates.
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2023
ISSN: ['1534-0392', '1553-5258']
DOI: https://doi.org/10.3934/cpaa.2023010