In this Section, we investigate the local Sobolev regularity of Du. Unlike in the periodic case, where we prove that a-priori Du∈L∞(Td), here we obtain a weaker bound, namely Du∈Lploc(Rd). We start by establishing some preliminary estimates.
In this section we shall introduce a relaxed formulation of the system (4.2)–(4.4) that avoids the explicit presence of the pressure variable. In this way we can overcome the solvability issues in the Poisson equation (4.4) due to the possible degen…
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