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Second Order Elliptic Equations in \(\mathbb{R}^{d} \) with Piecewise Continuous Coefficients

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Abstract

The existence and uniqueness of solutions of second order elliptic differential equations in \(\mathbb{R}^{d} \) are proved. The coefficients of second order terms are allowed to have discontinuity at finitely many parallel hyper-planes in \(\mathbb{R}^{d} \) and the first derivatives of solutions can have jumps at the hyper-planes.

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  1. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada

    Doyoon Kim

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  1. Doyoon Kim
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Kim, D. Second Order Elliptic Equations in \(\mathbb{R}^{d} \) with Piecewise Continuous Coefficients. Potential Anal 26, 189–212 (2007). https://doi.org/10.1007/s11118-006-9034-0

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  • DOI: https://doi.org/10.1007/s11118-006-9034-0

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