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@article{faucris.112721004,
abstract = {We establish partial regularity for solutions (u, π): ℝ ^{n} ×ℝ ^{n} ⊇ Ω × Σ → ℝ ^{n} × ℝ to systems modeling electro-rheological fluids in the stationary case. As a model case our result covers the low order regularity of systems of the type (equation) where εu denotes the symmetric part of the gradient Du, π denotes the pressure, the not necessarily continuous coefficient μ is a bounded non-negative VMO-function and the variable exponent function p: Ω → (3n/n+2, ∞) fulfills the logarithmic continuity assumption, i.e., we assume that for the modulus of continuity ω p of the exponent function p there holds (equation) To be more precise, we prove Hölder continuity of the solution u outside of a negligible set. Moreover, we show that εu and the pressure belong to certain Morrey spaces on the regular set of u, i.e., the set where u is Hölder continuous. Note that under such weak assumptions partial Hölder continuity for the gradient cannot be expected. Our result is even new if the coefficient μ is continuous. © de Gruyter 2012.},
author = {Bögelein, Verena and Duzaar, Frank and Habermann, Jens and Scheven, Christoph},
doi = {10.1515/ACV.2011.009},
faupublication = {yes},
journal = {Advances in Calculus of Variations},
keywords = {Electro-rheological fluids; Non-standard growth condition; Partial Hölder-and Morrey-type regularity; VMO-coefficients},
note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.lma2.statio},
pages = {1-57},
peerreviewed = {Yes},
title = {{Stationary} electro-rheological fluids: {Low} order regularity for systems with discontinuous coefficients},
volume = {5},
year = {2012}
}