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arXiv · 1903.06443

Solenoidal difference quotients and their application to the regularity theory of the $p$-Stokes system

Martin Křepela·Michael Růžička
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Abstract

We prove existence of a solution to the divergence equation satisfying a new Bogovski-type estimate for the difference quotients. This enables us to give an alternative proof of the interior regularity of the solution to the $p$-Stokes problem, completely avoiding the pressure. Moreover, as a key preliminary result we prove boundedness of Calder\'on-Zygmnud operators with standard kernels in weighted Lebesgue and Orlicz spaces over a general domain.

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Martin Křepela, Michael Růžička. 2019-03-15. Solenoidal difference quotients and their application to the regularity theory of the $p$-Stokes system. https://arxiv.org/abs/1903.06443

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