Abstract
We study equations in divergence form with piecewise Cα coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise C1,α estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
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Chen’s research was supported by National Natural Science Foundation of China (12061080, 12161087 and 12261093) and the Science and Technology Project of the Education Department of Jiangxi Province (GJJ211601). Deng’s research was supported by National Natural Science Foundation of China (11871305).
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Chen, J., Deng, X. Elliptic equations in divergence form with discontinuous coefficients in domains with corners. Acta Math Sci 44, 1903–1915 (2024). https://doi.org/10.1007/s10473-024-0515-2
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DOI: https://doi.org/10.1007/s10473-024-0515-2