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Homogenization of elliptic PDE with L1source term in domains with boundary having very general oscillations

Nandakumaran, AK and Sufian, A and Thazhathethil, R (2023) Homogenization of elliptic PDE with L1source term in domains with boundary having very general oscillations. In: Asymptotic Analysis, 133 (1-2). pp. 123-158.

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Official URL: https://doi.org/10.3233/ASY-221808


In the present article, we study the homogenization of a second-order elliptic PDE with oscillating coefficients in two different domains, namely a standard rectangular domain with very general oscillations and a circular type oscillating domain. Further, we consider the source term in L 1 and hence the solutions are interpreted as renormalized solutions. In the first domain, oscillations are in horizontal directions, while that of the second one is in the angular direction. To take into account the type of oscillations, we have used two different types of unfolding operators and have studied the asymptotic behavior of the renormalized solution of a second-order linear elliptic PDE with a source term in L 1 . In fact, we begin our study in oscillatory circular domain with oscillating coefficients and L 2 data which is also new in the literature. We also prove relevant strong convergence (corrector) results. We present the complete details in the context of circular domains, and sketch the proof in other domain. © 2023 - IOS Press. All rights reserved.

Item Type: Journal Article
Publication: Asymptotic Analysis
Publisher: IOS Press BV
Additional Information: The copyright for this article belongs to the IOS Press BV.
Keywords: Circular domains; Circular oscillating domain; Different domains; Elliptic PDEs; Homogenization; Oscillating boundaries; Periodic unfolding; Renormalized solutions; Second order elliptic; Source terms, Asymptotic analysis
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 06 Nov 2023 04:03
Last Modified: 06 Nov 2023 04:03
URI: https://eprints.iisc.ac.in/id/eprint/83065

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