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We study nonlinear elliptic equations of p(x)-Laplacian type on nonsmooth domains to obtain an optimal Calderón–Zygmund type estimate in the variable exponent spaces. We find a correct regularity assumption on p(⋅), a minimal regularity requirement on the associated nonlinearity and a suitable flatness condition on the boundary of the underlying domain for such W1,q(⋅) regularity theory to hold true...
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