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Regularity of solutions to a non homogeneous boundary value problem for general Stokes systems in Rn+

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Abstract.

We give a simple and very complete proof of the existence of a strong (H2) solution to the non-homogeneous problem (1.1) under the non homogeneous boundary conditions (1.6). Here we consider the half-space case Ω = Rn+, n≥ 3, see theorem 1.2. This regularity result was previously obtained by Solonnikov and Ščadilov in reference [33] for the classical Stokes system (μ=λ=0, g(x)=0) in the 3−D homogenous case (a=0, b=0) and Ω a suitable open subset of R3.

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  1. Dipartimento di Matematica Applicata “U. Dini”, Università di Pisa, Via Bonanno 25/B, 56126, Pisa, Italy

    H. Beirão da Veiga

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Partly supported by CMAF/UL and FCT.

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Beirão da Veiga, H. Regularity of solutions to a non homogeneous boundary value problem for general Stokes systems in Rn+. Math. Ann. 331, 203–217 (2005). https://doi.org/10.1007/s00208-004-0578-2

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