Murat Akman

activity

20132026

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

24 citations · 42 across the 15 of their papers we have counts for

collaborators

18 papers

math.AP2026

Brunn-Minkowski Inequality for p-Harmonic Measures

Ariel A. Aguas-Barreno, Murat Akman, Shirsho Mukherjee

We prove a Brunn--Minkowski inequality for a functional associated with p-harmonic measures for $1 < p < n + 1$ , on a class of convex domains satisfying suitable conditions. Under an add…

math.AP2023★ 1 cited

On the Minkowski problem for p-harmonic measures

Murat Akman, Shirsho Mukherjee

We study the Minkowski problem corresponding to the p-harmonic measures and obtain results previously known for harmonic measures due to Jerison. We show that a class of Borel meas…

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.CA2021

Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition

Murat Akman, Steve Hofmann, José María Martell +1

Let $Ω \subset R^{n + 1}$ , $n \geq 2$ , be a 1-sided non-tangentially accessible domain (aka uniform domain), that is, $Ω$ satisfies the interior Corkscrew and Harnack chain cond…

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.CA2019

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

Murat Akman, Steve Hofmann, José María Martell +1

Let $Ω \subset R^{n + 1}$ , $n \geq 2$ , be a 1-sided non-tangentially accessible domain (aka uniform domain), i.e., a set which satisfies the interior Corkscrew and Harnack chain…

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.CA2016

Absolute continuity of harmonic measure for domains with lower regular boundaries

Murat Akman, Jonas Azzam, Mihalis Mourgoglou

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

math.CA2016★ 10 cited

Rectifiability, interior approximation and Harmonic Measure

Murat Akman, Simon Bortz, Steve Hofmann +1

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

math.AP2015★ 1 cited

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

Murat Akman

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

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…

math.CA2015★ 24 cited

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

Murat Akman, Matthew Badger, Steve Hofmann +1

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

math.AP2013

Hausdorff dimension and $σ$ finiteness of $p -$ harmonic measures in space when $p \geq n$

Murat Akman, John Lewis, Andrew Vogel

In this paper we study a p harmonic measure, associated with a positive p harmonic function \hat{u} defined in an open set O, subset of R^n, and vanishing on a portion Γof boundary…

math.AP2013

On the dimension of a certain measure in the plane

Murat Akman

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 gen…

Brunn-Minkowski Inequality for p-Harmonic Measures

On the Minkowski problem for p-harmonic measures

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

Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition

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

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

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

Absolute continuity of harmonic measure for domains with lower regular boundaries

Rectifiability, interior approximation and Harmonic Measure

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

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

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

Hausdorff dimension and σ finiteness of p−harmonic measures in space when p≥n

On the dimension of a certain measure in the plane

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

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

Hausdorff dimension and $σ$ finiteness of $p -$ harmonic measures in space when $p \geq n$