| Title:
|
On the regularity of local minimizers of decomposable variational integrals on domains in $\Bbb R^2$ (English) |
| Author:
|
Bildhauer, M. |
| Author:
|
Fuchs, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
321-341 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider local minimizers $u : \Bbb R^2\supset \Omega \to \Bbb R^N$ of variational integrals like $\int_\Omega [(1+|\partial_1 u|^{2})^{p/2}+(1+|\partial_2 u|^{2})^{q/2}]\,dx$ or its degenerate variant $\int_\Omega [|\partial_1 u|^p+|\partial_2 u|^q]\,dx$ with exponents $2\leq p < q < \infty $ which do not fall completely in the category studied in Bildhauer M., Fuchs M., Calc. Var. {\bf 16} (2003), 177--186. We prove interior $C^{1,\alpha}$- respectively $C^{1}$-regularity of $u$ under the condition that $q < 2p$. For decomposable variational integrals of arbitrary order a similar result is established by the way extending the work Bildhauer M., Fuchs M., Ann. Acad. Sci. Fenn. Math. {\bf 31} (2006), 349--362. (English) |
| Keyword:
|
non-standard growth |
| Keyword:
|
vector case |
| Keyword:
|
local minimizers |
| Keyword:
|
interior regularity |
| Keyword:
|
problems of higher order |
| MSC:
|
35J35 |
| MSC:
|
35J50 |
| MSC:
|
49N60 |
| idZBL:
|
Zbl 1199.49075 |
| idMR:
|
MR2338100 |
| . |
| Date available:
|
2009-05-05T17:03:16Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119662 |
| . |
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