The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems

By Hansol Hong, Deping Ye, Ning Zhang. 2017

53 citations recorded by the source corpus.

In this paper, combining the p-capacity for $$p\in (1, n)$$p∈(1,n) with the Orlicz addition of convex domains, we develop the p-capacitary Orlicz–Brunn–Minkowski theory. In particular, the Orlicz $$L_{\phi }$$Lϕ mixed p-capacity of two convex domains is introduced and its geometric interpretation is obtained by the p-capacitary Orlicz–Hadamard variational formula. The p-capacitary Orlicz–Brunn–Minkowski and Orlicz–Minkowski inequalities are established, and the equivalence of these two inequalities are discussed as well. The p-capacitary Orlicz–Minkowski problem is proposed and solved under some mild conditions on the involving functions and measures. In particular, we provide the solutions for the normalized p-capacitary $$L_q$$Lq Minkowski problems with $$q>1$$q>1 for both discrete and general measures.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f152bcde7a6e980ef6e646d2cdbfa59f9f7034f6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yiming Zhao
2. Yong Huang
3. Dongmeng Xi
4. Qi-Rui Li
5. Haodi Chen
6. Shibing Chen
7. Deping Ye
8. Jian Lu

Citations in the corpus

• The Minkowski problem in Gaussian probability space (2020, result): “See also [22,36,40,48,71,78] for additional results and contributions in the Orlicz extension of the classical Brunn-Minkowski theory.”