Lq-Estimates for stationary Stokes system with coefficients measurable in one direction Article Swipe

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Lipschitz continuity Bounded function Mathematics Measurable function Mathematical analysis Ball (mathematics) A priori and a posteriori Space (punctuation) Constant (computer programming) Linguistics Computer science Programming language Philosophy Epistemology

Hongjie Dong , Doyoon Kim ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.1142/s1664360719500048 · OA: W2335863451

We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori [Formula: see text]-estimates for any [Formula: see text] when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a [Formula: see text]-estimate and prove the solvability for any [Formula: see text] when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.