Estimates for $k$-Hessian operator and some applications

Title:

Estimates for $k$-Hessian operator and some applications

Creator:

Wan, Dongrui

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:d1aaa3e3-01b4-4797-bcfa-1a9659a9226a
uuid:d1aaa3e3-01b4-4797-bcfa-1a9659a9226a

Subject:

$k$-convex function, $k$-Hessian operator, $k$-Hessian measure, and $k$-Green function

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

547-564

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:2

Harvested from:

CDK

Metadata only:

false