# The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity

@article{Akman2022TheBI, title={The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity}, author={Murat Akman and Jasun Gong and Jay Hineman and Johnny M. Lewis and Andrew Vogel}, journal={Memoirs of the American Mathematical Society}, year={2022} }

<p>In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, <inline-formula content-type="math/mathml">
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<mml:mi>Cap</mml:mi>
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<mml:mrow class="MJX…

## 24 Citations

On the Discrete Orlicz Electrostatic
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<jats:p>We establish the existence of solutions to the Orlicz electrostatic <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M2">
<mi>q</mi>
</math>…

The Lp Minkowski problem for q-capacity

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- 2021

In the present paper, we first introduce the concepts of the Lp q-capacity measure and Lp mixed q-capacity and then prove some geometric properties of Lp q-capacity measure and a Lp Minkowski…

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In this article we study two classical problems in convex geometry associated to $\mathcal{A}$-harmonic PDEs, quasi-linear elliptic PDEs whose structure is modeled on the $p$-Laplace equation. Let…

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- 2019

Abstract In this article we study two classical problems in convex geometry associated to 𝒜{\mathcal{A}}-harmonic PDEs, quasi-linear elliptic PDEs whose structure is modelled on the p-Laplace…

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

- Mathematics
- 2017

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…

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- Mathematics
- 2020

In the present paper, we first introduce the concepts of the Lpn-dimensional Logarithmic-Capacity measure and Lp mixed n-dimensional Logarithmic-Capacity and then prove some geometric properties of…

Minkowski problem for the electrostatic p-capacity for p > n

- Mathematics
- 2020

The setting for this article is the Euclidean n-space R. A convex body in R is a compact convex set with nonempty interior. A polytope in R is the convex hull of a finite set of points in R, provided…

Note on an eigenvalue problem with applications to a Minkowski type regularity problem in $${\mathbb {R}}^{n}$$

- MathematicsCalculus of Variations and Partial Differential Equations
- 2020

We consider existence and uniqueness of homogeneous solutions $ u > 0 $ to certain PDE of $p$-Laplace type, $ p $ fixed, $ n - 1 \cos \alpha \, | x| \} \quad \mbox{for fixed}\, \, \alpha \in (0, \pi…

Note on an eigenvalue problem for an ODE originating from a homogeneous $p$-harmonic function

- Mathematics
- 2020

We discuss what is known about homogeneous solutions $ u $ to the p-Laplace equation, $ p $ fixed, $1 or $ u > 0 $ is p-harmonic in the cone, \[ K(\alpha) = \{ x = (x_1, \dots, x_n ) : x_1 > \cos…

NOTE ON AN EIGENVALUE PROBLEM WITH APPLICATIONS TO A MINKOWSKI TYPE REGULARITY PROBLEM IN R

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- 2019

We consider existence and uniqueness of homogeneous solutions u > 0 to certain PDE of p-Laplace type, p fixed, n − 1 < p < ∞, n ≥ 2, when u is a solution in K(α) ⊂ R where K(α) := {x = (x1, . . . ,…

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Abstract
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