| Title:
|
Weighted Miranda-Talenti inequality and applications to equations with discontinuous coefficients (English) |
| Author:
|
Leonardi, S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
43-59 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Omega $ be an open bounded set in $\Bbb R^{n}$ $(n\geq 2)$, with $C^2$ boundary, and $N^{p,\lambda}(\Omega )$ ($1 < p < +\infty $, $0\leq \lambda < n$) be a weighted Morrey space. In this note we prove a weighted version of the Miranda-Talenti inequality and we exploit it to show that, under a suitable condition of Cordes type, the Dirichlet problem: $$ \cases \sum_{i,j=1}^n a_{ij}(x) \frac{\partial ^2 u}{\partial x_i \partial x_j} = f(x) \in N^{p,\lambda }(\Omega) \quad & \text{ in } \Omega \ u=0 & \text{ on } \partial \Omega \endcases $$ has a unique strong solution in the functional space $$ \left\{ u \in W^{2,p} \cap W^{1,p}_o(\Omega ) : \frac{\partial ^2 u}{\partial x_i \partial x_j} \in N^{p,\lambda}(\Omega ), i,j=1,2,\,\ldots, n\right\}. $$ (English) |
| Keyword:
|
Miranda-Talenti inequality |
| Keyword:
|
nonvariational elliptic equations |
| Keyword:
|
Hölder regularity |
| MSC:
|
35B45 |
| MSC:
|
35B65 |
| MSC:
|
35J25 |
| MSC:
|
35J60 |
| MSC:
|
35R05 |
| idZBL:
|
Zbl 1090.35045 |
| idMR:
|
MR1903306 |
| . |
| Date available:
|
2009-01-08T19:19:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119299 |
| . |
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