| Title:
|
Gradient estimates for elliptic systems in Carnot-Carathéodory spaces (English) |
| Author:
|
Di Fazio, Giuseppe |
| Author:
|
Fanciullo, Maria Stella |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
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43 |
| Issue:
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4 |
| Year:
|
2002 |
| Pages:
|
605-618 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X=(X_1,X_2,\dots ,X_q)$ be a system of vector fields satisfying the Hör\-man\-der condition. We prove $L^{2,\lambda}_X$ local regularity for the gradient $Xu$ of a solution of the following strongly elliptic system $$ -X^{*}_{\alpha }(a^{\alpha \beta }_{ij}(x)X_{\beta } u^{j})= g_{i}-X^{*}_{\alpha } f^{\alpha }_{i}(x) \quad \forall i=1,2,\dots ,N, $$ where $a^{\alpha \beta }_{ij}(x)$ are bounded functions and belong to Vanishing Mean Oscillation space. (English) |
| Keyword:
|
elliptic systems |
| Keyword:
|
Morrey space regularity |
| Keyword:
|
Carnot-Carathéodory metric |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35H20 |
| MSC:
|
35J45 |
| MSC:
|
35J50 |
| idZBL:
|
Zbl 1090.35058 |
| idMR:
|
MR2045784 |
| . |
| Date available:
|
2009-01-08T19:25:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119351 |
| . |
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| . |
