| Title:
|
Quasiharmonic fields and Beltrami operators (English) |
| Author:
|
Capone, Claudia |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
363-377 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A quasiharmonic field is a pair $\Cal{F} = [B,E]$ of vector fields satisfying $\operatorname{div} B=0$, $\operatorname{curl} E=0$, and coupled by a distorsion inequality. For a given $\Cal F$, we construct a matrix field $\Cal A=\Cal A[B,E]$ such that ${\Cal A} E=B$. This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator $\Cal A[B,E]$ and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence. (English) |
| Keyword:
|
quasiharmonic fields |
| Keyword:
|
Beltrami operator |
| Keyword:
|
elliptic partial differential equations |
| Keyword:
|
G-convergence |
| MSC:
|
30C65 |
| MSC:
|
35B40 |
| MSC:
|
35B45 |
| MSC:
|
35D10 |
| MSC:
|
35J20 |
| MSC:
|
35J60 |
| MSC:
|
47B99 |
| MSC:
|
47F05 |
| idZBL:
|
Zbl 1069.35024 |
| idMR:
|
MR1922134 |
| . |
| Date available:
|
2009-01-08T19:22:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119326 |
| . |
| Reference:
|
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| . |
