Johnny M. Lewis

activity

20182021

collaborators

3 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.AP2018

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…

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

On a Theorem of Wolff Revisited

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

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

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