| Title:
|
Estimates for $k$-Hessian operator and some applications (English) |
| Author:
|
Wan, Dongrui |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
547-564 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The $k$-convex functions are the viscosity subsolutions to the fully nonlinear elliptic equations $F_{k}[u]=0$, where $F_{k}[u]$ is the elementary symmetric function of order $k$, $1\leq k\leq n$, of the eigenvalues of the Hessian matrix $D^{2}u$. For example, $F_{1}[u]$ is the Laplacian $\Delta u$ and $F_{n}[u]$ is the real Monge-Ampère operator det $D^{2}u$, while $1$-convex functions and $n$-convex functions are subharmonic and convex in the classical sense, respectively. In this paper, we establish an approximation theorem for negative $k$-convex functions, and give several estimates for the mixed $k$-Hessian operator. Applications of these estimates to the $k$-Green functions are also established. (English) |
| Keyword:
|
$k$-convex function |
| Keyword:
|
$k$-Hessian operator |
| Keyword:
|
$k$-Hessian measure |
| Keyword:
|
$k$-Green function |
| MSC:
|
31A05 |
| MSC:
|
31A15 |
| MSC:
|
47J20 |
| MSC:
|
58C35 |
| idZBL:
|
Zbl 06236431 |
| idMR:
|
MR3073978 |
| DOI:
|
10.1007/s10587-013-0037-x |
| . |
| Date available:
|
2013-07-18T15:10:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143332 |
| . |
| Reference:
|
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| Reference:
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| . |
