Murat Akman

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20132022

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7 papers · 1 filter

math.AP2022

Borderline gradient continuity for the normalized $p$ -parabolic operator

Murat Akman, Agnid Banerjee, Isidro H. Munive

In this paper, we prove gradient continuity estimates for viscosity solutions to $Δ_{p}^{N} u - u_{t} = f$ in terms of the scaling critical $L (n + 2, 1)$ norm of $f$ , where $Δ_{p}^{N}$ is th…

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

On a Bernoulli-type overdetermined free boundary problem

Murat Akman, Agnid Banerjee, Mariana Smit Vega Garcia

In this article we study a Bernoulli-type free boundary problem and generalize a work of Henrot and Shahgholian in \cite{HS1} to $A$ -harmonic PDEs. These are quasi-linear…

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

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…

Borderline gradient continuity for the normalized p-parabolic operator

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

On a Theorem of Wolff Revisited

On a Bernoulli-type overdetermined free boundary problem

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

Borderline gradient continuity for the normalized $p$ -parabolic operator

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