Higher differentiability for solutions of stationary p‐Stokes systems

Flavia Giannetti, Antonia Passarelli di Napoli and Christoph Scheven

Mathematische Nachrichten, 2020, vol. 293, issue 11, 2082-2111

Abstract: We consider weak solutions (u,π):Ω→Rn×R to stationary p‐Stokes systems of the type −diva(x,Eu)+∇π+[Du]u=f,divu=0in Ω⊂Rn, where the function a(x,ξ) satisfies p‐growth conditions in ξ and depends Hölder continuously on x. By Eu we denote the symmetric part of the gradient Du and we write [Du]u for the convective term. In this setting, we establish results on the fractional higher differentiability of both the symmetric part of the gradient Eu and of the pressure π. As an application, we deduce dimension estimates for the singular set of the gradient Du, thereby improving known results on partial C1,α‐regularity for solutions to stationary p‐Stokes systems.

Date: 2020
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https://doi.org/10.1002/mana.201800519

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