Can I read $L^p$ Christoffel-Minkowski problem: the case $1< p<k+1$ on EtoBox?

$L^p$ Christoffel-Minkowski problem: the case $1< p<k+1$ by Guan, Pengfei; Xia, Chao is a scholarly article available to read on EtoBox.

What is $L^p$ Christoffel-Minkowski problem: the case $1< p<k+1$ about?

We consider a fully nonlinear partial differential equation associated to the intermediate $L^p$ Christoffel-Minkowski problem in the case $1<p<k+1$. We establish the existence of convex body with prescribed $k$-th even $p$-area measure on $\mathbb S^n$, under an appropriate assumption on the prescribed function. We construct examples to indicate certain geometric condition on the prescribed function is needed for the existence of smooth strictly convex body. We also obtain $C^{1,1}$ regularity estimates for admissible solutions of the equation when $ p\ge \frac{k+1}2$.

Author

Guan, Pengfei; Xia, Chao

Published

2017

Language

EN