Abstract
We establish global W 1, p(·)-estimates for second order elliptic equations in divergence form under the natural assumption that p(·) is log-Hölder continuous. To this end, we assume that the coefficients are measurable in one variable and have small BMO semi-norms in the other variables and the boundary of the domain is Reifenberg flat. Our work is an optimal and natural extension of W 1,p-regularity for such equations with merely measurable coefficients beyond Lipschitz domains.
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Byun, SS., Ok, J. & Wang, L. W 1, p(·)-Regularity for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains. Commun. Math. Phys. 329, 937–958 (2014). https://doi.org/10.1007/s00220-014-1962-8
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DOI: https://doi.org/10.1007/s00220-014-1962-8