Solenoidal difference quotients and their application to the regularity theory of the $p$-Stokes system
Analysis of PDEs
2019-10-28 v2 Functional Analysis
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 -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.
Keywords
Cite
@article{arxiv.1903.06443,
title = {Solenoidal difference quotients and their application to the regularity theory of the $p$-Stokes system},
author = {Martin Křepela and Michael Růžička},
journal= {arXiv preprint arXiv:1903.06443},
year = {2019}
}