| Title:
|
A global differentiability result for solutions of nonlinear elliptic problems with controlled growths (English) |
| Author:
|
Fattorusso, Luisa |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
113-129 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Omega $ be a bounded open subset of $\mathbb{R}^{n}$, $n>2$. In $\Omega $ we deduce the global differentiability result \[ u \in H^{2}(\Omega , \mathbb{R}^{N}) \] for the solutions $u \in H^{1}(\Omega , \mathbb{R}^{n})$ of the Dirichlet problem \[ u-g \in H^{1}_{0}(\Omega , \mathbb{R}^{N}), -\sum _{i}D_{i}a^{i}(x,u,Du)=B_{0}(x,u,Du) \] with controlled growth and nonlinearity $q=2$. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure. (English) |
| Keyword:
|
global differentiability of weak solutions |
| Keyword:
|
elliptic problems |
| Keyword:
|
controlled growth |
| Keyword:
|
nonlinearity with $q=2$ |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35J60 |
| MSC:
|
58B10 |
| idZBL:
|
Zbl 1174.35039 |
| idMR:
|
MR2402529 |
| . |
| Date available:
|
2009-09-24T11:53:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128249 |
| . |
| Reference:
|
[1] S. Campanato: Equazioni ellittiche del $II^{\circ }$ ordine e spazi $L^{2,\lambda }$.Ann. Mat. Pura App. 69 (1965), 321–382. (Italian) MR 0192168, 10.1007/BF02414377 |
| Reference:
|
[2] S. Campanato: Sistemi ellittici in forma di divergenza.Quad. Scuola Normale Superiore Pisa (1980). (English) MR 0668196 |
| Reference:
|
[3] S. Campanato: Differentiability of the solutions of nonlinear elliptic system with natural growts.Ann. Mat. Pura Appl., 4. Ser. 131 (1982), 75–106. MR 0681558, 10.1007/BF01765147 |
| Reference:
|
[4] S. Campanato: A maximum principle for nonlinear elliptic system: Boundary fundamental estimates.Adv. Math. 66 (1987), 291–317. MR 0915857, 10.1016/0001-8708(87)90037-5 |
| Reference:
|
[5] S. Campanato, P. Cannarsa: Differentiability and partial Hölder continuity of the solutions of non linear elliptic systems of order $2m$ with quadratic growth.Ann. Sc. Norm. Super. Pisa Cl. Sci., IV. Ser. 8 (1981), 285–309. MR 0623938 |
| . |
