The L dual Minkowski problem for p > 1 and q > 0
By K. Boroczky, Ferenc Fodor. Journal of Differential Equations, 2018
100 citations recorded by the source corpus.
General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang. These new measures unify several other geometric measures of the Brunn-Minkowski theory and the dual Brunn-Minkowski theory. $L_p$ dual curvature measures arise from $q$th dual inrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang formulated the $L_p$ dual Minkowski problem, which concerns the characterization of $L_p$ dual curvature measures. In this paper, we solve the existence part of the $L_{p}$ dual Minkowski problem for $p>1$ and $q>0$, and we also discuss the regularity of the solution.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/611177f69c89868381bbe2c10380b13cf4b1ef4a
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
Citations in the corpus
- The Lp dual Minkowski problem and related parabolic flows (2021, methodology): “9) was resolved by Böröczky and Fodor [8], provided p > 1, q > 0 and μ ∈ NCH.”
- Variations of a class of Monge–Ampère-type functionals and their applications (2021, background): “3) was partially addressed in [6, 12, 14, 26], and the uniqueness of solutions was proved for p > q [26, 33].”
- A flow method for the dual Orlicz–Minkowski problem (2020, background): “After the Lp dual Minkowski problem was first proposed in [57], several existence results of solutions were established in [4, 12, 35].”