Abstract
We prove an Lq theory result for generalized Stokes system in a \({\mathcal{C}^{2,1}}\) domain complemented with the perfect slip boundary conditions and under Φ-growth conditions. Since the interior regularity was obtained in Diening and Kaplický (Manu Math 141:336–361, 2013), a regularity up to the boundary is an aim of this paper. In order to get the main result, we use Calderon–Zygmund theory and the method developed in Caffarelli and Peral (Ann Math 130:189–213, 1989). We obtain higher integrability of the first gradient of a solution.
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