FRACTIONAL HIGHER DIFFERENTIABILITY OF SOLUTIONS TO THE STATIONARY ORLICZ-STOKES SYSTEM

This work concerns the stationary Stokes system subject to Orlicz type growth conditions. Fractional regularity properties of the symmetric gradient of local solutions are established, depending on a balance between the nonlinearity of the differential operator and the degree of integrability of the right-hand side in Orlicz spaces. This regularity is described via the membership of a non linear expression of the symmetric gradient in Besov spaces. The fractional regularity of the pressure term is also exhibited and is formulated in terms of Orlicz-Besov spaces. Parallel results for the symmetric gradient of local solutions to the associated plain elliptic system are also offered. A new version of a Poincar´e-Sobolev inequality in Orlicz spaces, in modular form, on domains with finite measure plays a role in the proofs.