| Title:
|
Recent results on quasilinear differential equations. I (English) |
| Author:
|
Drábek, Pavel |
| Language:
|
English |
| Journal:
|
Nonlinear Analysis, Function Spaces and Applications |
| Volume:
|
Vol. 9 |
| Issue:
|
2010 |
| Year:
|
|
| Pages:
|
1-29 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This lecture follows a joint result of the speaker and Daniel Daners. To make the exposition clear and transparent we concentrate here only on the $L_\infty$-estimates for weak solutions for the $p$-Laplacian with all standard boundary conditions on possibly non-smooth domains. We present $C^{1,\alpha}$-regularity and maximum principle for weak solutions as an application. We also prove existence, continuity and compactness of the resolvent operator. (English) |
| Keyword:
|
quasi-linear problems; $p$-Laplacian; $L_\infty$-estimates; non-smooth domains; Moser iterations |
| MSC:
|
35B45 |
| MSC:
|
35B65 |
| MSC:
|
35J65 |
| MSC:
|
35J70 |
| . |
| Date available:
|
2013-03-04T13:31:07Z |
| Last updated:
|
2013-03-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702636 |
| . |
