We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.
@article{bwmeta1.element.doi-10_2478_s11533-011-0047-6,
author = {V\'aclav M\'acha},
title = {On a generalized Stokes problem},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {874-887},
zbl = {1233.35060},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0047-6}
}
Václav Mácha. On a generalized Stokes problem. Open Mathematics, Tome 9 (2011) pp. 874-887. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0047-6/
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