Partial Hölder continuity for discontinuous elliptic problems with VMO‐coefficients

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Higher differentiability of minimizers of variational integrals with Sobolev coefficients (2012, background): “Since our goal is to obtain the regularity at level of the gradient of the minimizer (not of the function itself as in the above quoted papers), with respect to the hypotheses of [4], we have to assume a slightly stronger regularity for the integrand F with respect to x, still dealing with the case ”
Pointwise Calderón–Zygmund gradient estimates for the p -Laplace system (2015, background): “For instance, results on elliptic problems involving differential operators affected by weak regularity properties can be found in [24, 25, 7, 35, 36].”
Higher Differentiability of Solutions of Elliptic Systems with Sobolev Coefficients: The Case p = n = 2 (2014, background): “Very recently, the result of [14] has been extended in [4] to operators that have discontinuous dependence on the x-variable, through a VMO coefficient.”