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

- M. Akman, J. Gong, Jay Hineman, Johnny M. Lewis, A. Vogel
- MathematicsMemoirs of the American Mathematical Society
- 1 September 2017

<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… Expand

Rectifiability, interior approximation and harmonic measure

- M. Akman, S. Bortz, S. Hofmann, J. M. Martell
- MathematicsArkiv för Matematik
- 29 January 2016

We prove a structure theorem for any $n$-rectifiable set $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, satisfying a weak version of the lower ADR condition, and having locally finite $H^n$ ($n$-dimensional… Expand

Absolute continuity of harmonic measure for domains with lower regular boundaries

- M. Akman, Jonas Azzam, Mihalis Mourgoglou
- MathematicsAdvances in Mathematics
- 24 May 2016

We study absolute continuity of harmonic measure with respect to surface measure on domains $\Omega$ that have large complements. We show that if $\Gamma\subset \mathbb{R}^{d+1}$ is $d$-Ahlfors… Expand

Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition

- M. Akman, S. Hofmann, J. M. Martell, T. Toro
- Mathematics
- 24 January 2019

Let $\Omega\subset\mathbb{R}^{n+1}$, $n\ge 2$, be a 1-sided non-tangentially accessible domain (aka uniform domain), that is, a set which satisfies the interior Corkscrew and Harnack chain… Expand

Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries

- M. Akman, Matthew Badger, S. Hofmann, J. M. Martell
- Mathematics
- 8 July 2015

Let $\Omega \subset \mathbb{R}^{n+1}$, $n\geq 2$, be 1-sided NTA domain (aka uniform domain), i.e. a domain which satisfies interior Corkscrew and Harnack Chain conditions, and assume that… Expand

On the dimension of a certain measure in the plane

- M. Akman
- Mathematics
- 24 January 2013

We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane.
Our work generalizes work of… Expand

$\sigma$-finiteness of elliptic measures for quasilinear elliptic PDE in space

- M. Akman, Johnny M. Lewis, A. Vogel
- Mathematics
- 23 September 2015

In this paper we study the Hausdorff dimension of a elliptic measure $\mu_{f}$ in space associated to a positive weak solution to a certain quasilinear elliptic PDE in an open subset and vanishing on… Expand

On the logarithm of the minimizing integrand for certain variational problems in two dimensions

- M. Akman, John L. Lewis, A. Vogel
- Mathematics
- 24 January 2012

AbstractLet f be a smooth convex homogeneous function of degreep, 1 < p < ∞, on $${\mathbb{C} \setminus \{0\}.}$$ We show that if u is a minimizer for the functional whose integrand is $${f(\nabla v… Expand

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

- M. Akman, John L. Lewis, A. Vogel
- Mathematics
- 4 February 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… Expand

On the absolute continuity of p-harmonic measure and surface measure in Reifenberg flat domains

- M. Akman
- Mathematics
- 23 September 2015

In this paper, we study the set of absolute continuity of p-harmonic measure, $\mu$, and $(n-1)-$dimensional Hausdorff measure, $\mathcal{H}^{n-1}$, on locally flat domains in $\mathbb{R}^{n}$,… Expand

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