Lq theory for a generalized Stokes System

Regularity properties of solutions to the stationary generalized Stokes system are studied. The extra stress tensor is assumed to have a growth given by some N-function, which includes the situation of p -growth. We show results about differentiability of weak solutions. As a consequence we obtain t...

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Bibliographic Details
Published in:Manuscripta mathematica 2013, Vol.141 (1-2), p.333-361
Main Authors: Diening, L., Kaplický, P.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Summary:Regularity properties of solutions to the stationary generalized Stokes system are studied. The extra stress tensor is assumed to have a growth given by some N-function, which includes the situation of p -growth. We show results about differentiability of weak solutions. As a consequence we obtain the gradient L q estimates for the problem. These estimates are applied to the stationary generalized Navier Stokes equations.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-012-0574-x