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arXiv · 2011.13771

A non-local approach to the generalized Stokes operator with bounded measurable coefficients

Patrick Tolksdorf
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Abstract

We establish functional analytic properties of the Stokes operator with bounded measurable coefficients on $L^p_{\sigma} (\mathbb{R}^d)$, $d \geq 2$, for $\lvert 1 / p - 1 / 2 \rvert < 1 / d$. These include optimal resolvent bounds and the property of maximal $L^q$-regularity. We further give regularity estimates on the gradient of the solution to the Stokes resolvent problem with bounded measurable coefficients. As a key to these results we establish the validity of a non-local Caccioppoli inequality to solutions of the Stokes resolvent problem.

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Patrick Tolksdorf. 2020-11-27. A non-local approach to the generalized Stokes operator with bounded measurable coefficients. https://arxiv.org/abs/2011.13771

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