| Title:
|
Oblique derivative problem for elliptic equations in non-divergence form with $VMO$ coefficients (English) |
| Author:
|
di Fazio, G. |
| Author:
|
Palagachev, D. K. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
537-556 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A priori estimates and strong solvability results in Sobolev space $W^{2,p}(\Omega)$, $1<p<\infty$ are proved for the regular oblique derivative problem $$ \begin{cases} \sum_{i,j=1}^n a^{ij}(x)\frac{\partial^2u}{\partial x_i\partial x_j} =f(x) \text{ a.e. } \Omega \\ \frac{\partial u}{\partial \ell}+\sigma(x)u =\varphi(x) \text{ on } \partial \Omega \end{cases} $$ when the principal coefficients $a^{ij}$ are $V\kern -1.2pt MO\cap L^\infty$ functions. (English) |
| Keyword:
|
oblique derivative |
| Keyword:
|
elliptic equation |
| Keyword:
|
non divergence form |
| Keyword:
|
$V\kern -1.2pt MO$ coefficients |
| Keyword:
|
strong solution |
| MSC:
|
35J25 |
| idZBL:
|
Zbl 0881.35028 |
| idMR:
|
MR1426919 |
| . |
| Date available:
|
2009-01-08T18:26:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118861 |
| . |
| 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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| Reference:
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| Reference:
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| . |
