Abstract
We prove an L q 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 Calderón–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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Communicated by H. Beirao da Veiga
The authors would like to express their gratitude to Petr Kaplický for fruitful and inspiring discussions. Václav Mácha was supported by the Grant GAČR 201/09/0917 of Czech Science Foundation in the framework of RVO 67985840. Jakub Tichý was supported by the Grant GAČR 201/09/0917 of Czech Science Foundation, Grant 7AMB13DE001 of MEYES of the Czech Republic and partially by Grant SVV-2013-267316.
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Mácha, V., Tichý, J. Higher Integrability of Solutions to Generalized Stokes System Under Perfect Slip Boundary Conditions. J. Math. Fluid Mech. 16, 823–845 (2014). https://doi.org/10.1007/s00021-014-0190-5
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DOI: https://doi.org/10.1007/s00021-014-0190-5