Affiliation:
1. School of Mathematical Sciences, Zhejiang University , Hangzhou 310027 , China
Abstract
Abstract
This article concerns the
L
p
{L}_{p}
Minkowski problem for q-capacity. We consider the case
p
≥
1
p\ge 1
and
1
<
q
<
n
1\lt q\lt n
in the smooth category by a kind of curvature flow, which converges smoothly to the solution of a Monge-Ampére type equation. We show the existence of smooth solution to the problem for
p
≥
n
p\ge n
. We also provide a proof for the weak solution to the problem when
p
≥
1
p\ge 1
, which has been obtained by Zou and Xiong.
Subject
General Mathematics,Statistical and Nonlinear Physics
Reference33 articles.
1. M. Akman, J. S. Gong, J. Hineman, J. Lewis, and A. Vogel, The Brunn-Minkowski inequality and a Minkowski problem for nonlinear capacity, Memoirs American Math. Soc. 275 (2022), no. 1348, 1–128.
2. M. Akman, J. Lewis, O. Saari, and A. Vogel, The Brunn-Minkowski inequality and a Minkowski problem for A-harmonic Greenas function, Adv. Calc. Var. 14 (2021), no. 2, 247–302.
3. A. D. Aleksandrov, On the theory of mixed volumes. III. Extensions of two theorems of Minkowski on convex polyhedra to arbitrary convex bodies, Mat. Sb. (N.S.) 3 (1938), 27–46.
4. A. D. Aleksandrov, On the surface area measure of convex bodies, Mat. Sb. (N.S.) 6 (1939), 167–174.
5. L. A. Caffarelli, D. Jerison, and E. H. Lieb, On the case of equality in the Brunn-Minkowski inequality for capacity, Adv. Math. 117 (1996), 193–207.
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