5 citations · 6 across the 7 of their papers we have counts for
7 papers
On and problems for Newtonian potentials in Euclidean space
John Lewis
In this paper we first make and discuss a conjecture concerning Newtonian potentials in Euclidean n space which have all their mass on the unit sphere about the origin, and are nor…
Failure of Fatou type theorems for solutions to PDE of -Laplace type in domains with flat boundaries
Murat Akman, John Lewis, Andrew Vogel
Let denote Euclidean space and given a positive integer let , be a -dimensional plane…
On a Theorem of Wolff Revisited
Murat Akman, John Lewis, Andrew Vogel
We study -harmonic functions, , in and . We first s…
The Brunn-Minkowski inequality and a Minkowski problem for -harmonic Green's function
Murat Akman, John Lewis, Olli Saari +1
In this article we study two classical problems in convex geometry associated to -harmonic PDEs, quasi-linear elliptic PDEs whose structure is modeled on the -Lapla…
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 -capaci…
-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 in space associated to a positive weak solution to a certain quasilinear elliptic PDE in an open subset…
Hausdorff dimension and finiteness of harmonic measures in space when
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…