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On Lp-Resolvent Estimates for Second-Order Elliptic Equations in Divergence Form

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Abstract

We consider the Dirichlet problems for second-order linear elliptic equations in divergence form. The leading coefficient A has small BMO semi-norm and first-order coefficient b belongs to Lr, where \(n \leq r < \infty \) if n ≥ 3 and \(2 < r < \infty \) if n = 2. We first establish Lp-resolvent estimates on bounded domains having small Lipschitz constant when \(r/(r-1) < p < \infty \). Under the additional assumption div A ∈ Lr, we also establish Lp-resolvent estimates on bounded domains with C1,1 boundary when 1 < p < r.

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(No. NRF-2016R1D1A1B02015245).

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  1. Department of Mathematics, Sogang University, Seoul, 121–742, Korea

    Byungsoo Kang & Hyunseok Kim

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  1. Byungsoo Kang
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  2. Hyunseok Kim
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Correspondence to Hyunseok Kim.

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Kang, B., Kim, H. On Lp-Resolvent Estimates for Second-Order Elliptic Equations in Divergence Form. Potential Anal 50, 107–133 (2019). https://doi.org/10.1007/s11118-017-9675-1

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