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Application of Newton’s method to a homogenization problem

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Abstract

The homogenization of a family (P ε) of uniformly elliptic semilinear partial differential equations of second order is studied. The main result is that any non-singular solutionu of the homogenized problem (P) is the limit of non-singular solutions of (P ε). The method consists of specifying a functionw ε starting from which the Newton iterates converge to a solutionu ε ofP ε. These solutionsu ε converge to the given solutionu of (P).

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  1. TIFR Centre, Indian Institute of Science Campus, 560 012, Bangalore, India

    S. Kesavan

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  1. S. Kesavan
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Kesavan, S. Application of Newton’s method to a homogenization problem. Proc. Indian Acad. Sci. (Math. Sci.) 90, 229–238 (1981). https://doi.org/10.1007/BF02838078

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  • DOI: https://doi.org/10.1007/BF02838078

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