A. Vogel

activity

20132021

most citedThe Brunn-Minkowski inequality and a Minkowski problem for

A

-harmonic Green's function

5 citations · 6 across the 7 of their papers we have counts for

collaborators

7 papers

math.AP2021

Failure of Fatou type theorems for solutions to PDE of $p$ -Laplace type in domains with flat boundaries

Murat Akman, John Lewis, Andrew Vogel

Let $R^{n}$ denote Euclidean $n$ space and given $k$ a positive integer let $Λ_{k} \subset R^{n}$ , $1 \leq k < n - 1, n \geq 3,$ be a $k$ -dimensional plane…

math.AP2020

On a Theorem of Wolff Revisited

Murat Akman, John Lewis, Andrew Vogel

We study $p$ -harmonic functions, $1 < p \neq = 2 < \infty$ , in $R_{+}^{2} = {z = x + i y : y > 0, - \infty < x < \infty}$ and $B (0, 1) = {z : ∣ z ∣ < 1}$ . We first s…

math.AP2019

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

Murat Akman, John Lewis, Andrew Vogel

We consider existence and uniqueness of homogeneous solutions $u > 0$ to certain PDE of $p$ -Laplace type, $p$ fixed, $n - 1 < p < \infty, n \geq 2,$ when $u$ is a solution in…

math.AP2018★ 5 cited

The Brunn-Minkowski inequality and a Minkowski problem for $A$ -harmonic Green's function

Murat Akman, John Lewis, Olli Saari +1

In this article we study two classical problems in convex geometry associated to $A$ -harmonic PDEs, quasi-linear elliptic PDEs whose structure is modeled on the $p$ -Lapla…

math.AP2017★ 1 cited

The Brunn-Minkowski inequality and a Minkowski problem for nonlinear capacity

Murat Akman, Jasun Gong, Jay Hineman +2

In this article we study two classical potential-theoretic problems in convex geometry corresponding to a nonlinear capacity, $\mbox{Cap}_{\mathcal{A}}$, where $A$ -capaci…

math.AP2015

$σ$ -finiteness of elliptic measures for quasilinear elliptic PDE in space

Murat Akman, John Lewis, Andrew Vogel

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

Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries

On a Theorem of Wolff Revisited

Note on an eigenvalue problem with applications to a Minkowski type regularity problem in R^n

The Brunn-Minkowski inequality and a Minkowski problem for A-harmonic Green's function

The Brunn-Minkowski inequality and a Minkowski problem for nonlinear capacity

σ-finiteness of elliptic measures for quasilinear elliptic PDE in space

Failure of Fatou type theorems for solutions to PDE of $p$ -Laplace type in domains with flat boundaries

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

The Brunn-Minkowski inequality and a Minkowski problem for $A$ -harmonic Green's function

$σ$ -finiteness of elliptic measures for quasilinear elliptic PDE in space