| Title:
|
Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials (English) |
| Author:
|
Breit, Dominic |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
493-508 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss regularity results concerning local minimizers $u: \mathbb R^n\supset \Omega\rightarrow\mathbb R^n$ of variational integrals like \begin{align*} \int_{\Omega}\{F(\cdot ,\varepsilon (w))-f\cdot w\}\,dx \end{align*} defined on energy classes of solenoidal fields. For the potential $F$ we assume a $(p,q)$-elliptic growth condition. In the situation without $x$-dependence it is known that minimizers are of class $C^{1,\alpha }$ on an open subset $\Omega_{0}$ of $\Omega$ with full measure if $q< p\,\frac{n+2}{n}$ (for $n=2$ we have $\Omega_{0}=\Omega$). In this article we extend this to the case of nonautonomous integrands. Of course our result extends to weak solutions of the corresponding nonlinear Stokes type system. (English) |
| Keyword:
|
Stokes problem |
| Keyword:
|
generalized Newtonian fluids |
| Keyword:
|
regularity |
| Keyword:
|
nonautonomous functionals |
| Keyword:
|
local minimizer |
| MSC:
|
35B65 |
| MSC:
|
35J50 |
| MSC:
|
35Q35 |
| MSC:
|
49N60 |
| MSC:
|
76D07 |
| MSC:
|
76M30 |
| idZBL:
|
Zbl 06373980 |
| idMR:
|
MR3125072 |
| . |
| Date available:
|
2013-10-01T21:13:03Z |
| Last updated:
|
2016-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143472 |
| . |
| Reference:
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