| Title:
|
Differentiability for minimizers of anisotropic integrals (English) |
| Author:
|
Cavaliere, P. |
| Author:
|
D'Ottavio, A. |
| Author:
|
Leonetti, F. |
| Author:
|
Longobardi, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
685-696 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a function $u:\Omega \to \Bbb R^N$, $\Omega \subset \Bbb R^n$, minimizing the integral $\int_\Omega(|D_1 u|^2 + \dots +|D_{n-1}u|^2 +|D_n u|^p)\,dx$, $2(n+1)/(n+3)\leq p<2$, where $D_i u = \partial u/ \partial x_i$, or some more general functional with the same behaviour; we prove the existence of second weak derivatives $D(D_1 u), \dots , D(D_{n-1} u) \in L^2$ and $D(D_n u) \in L^p$. (English) |
| Keyword:
|
regularity |
| Keyword:
|
minimizers |
| Keyword:
|
integral functionals |
| Keyword:
|
anisotropic growth |
| MSC:
|
35J50 |
| MSC:
|
35J60 |
| MSC:
|
49N60 |
| idZBL:
|
Zbl 1060.49507 |
| idMR:
|
MR1715458 |
| . |
| Date available:
|
2009-01-08T18:47:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119044 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
