Article

Akman, Murat and Hofmann, Steve and Martell, José María and Toro, Tatiana (2022) 'Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition.' Advances in Calculus of Variations. ISSN 1864-8258

Akman, Murat and Lewis, John and Vogel, Andrew (2022) 'Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries.' Communications in Partial Differential Equations, 47 (7). pp. 1457-1503. ISSN 0360-5302

Akman, Murat and Lewis, J and Saari, O and Vogel, A (2021) 'The Brunn-Minkowski inequality and a Minkowski problem for A-harmonic Green's function.' Advances in Calculus of Variations, 14 (2). pp. 247-302. ISSN 1864-8258

Akman, Murat and Banerjee, Agnid and Vega Garcia, Mariana Smit (2021) 'On a Bernoulli-type overdetermined free boundary problem.' Annales Fennici Mathematici, 46 (2). pp. 601-618. ISSN 2737-0690

Akman, Murat and Lewis, John and Vogel, Andrew (2020) 'On a Theorem of Wolff Revisited.' Journal d'Analyse Mathematique. ISSN 0021-7670 (In Press)

Akman, Murat and Lewis, John and Vogel, Andrew (2019) 'Note on an eigenvalue problem with applications to a Minkowski type regularity problem in Rⁿ.' Calculus of Variations and Partial Differential Equations, 59 (2). ISSN 0944-2669 (In Press)

Akman, Murat and Bortz, Simon and Hofmann, Steve and Martell, José María (2019) 'Rectifiability, interior approximation and Harmonic measure.' Arkiv för Matematik, 57 (1). pp. 1-22. ISSN 0004-2080

Akman, Murat and Badger, Matthew and Hofmann, Steve and Martell, José María (2019) 'Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries.' Transactions of the American Mathematical Society, 369 (8). pp. 5711-5745. ISSN 0002-9947

Akman, Murat and Azzam, Jonas and Mourgoglou, Mihalis (2019) 'Absolute continuity of harmonic measure for domains with lower regular boundaries.' Advances in Mathematics, 345. pp. 1206-1252. ISSN 0001-8708

Akman, Murat and Lewis, John and Vogel, Andrew (2019) 'Note on an Eigenvalue problem for an ODE originating from a homogeneous p-harmonic function.' Algebra i Analiz, 31 (2). pp. 75-87. ISSN 0234-0852

Akman, Murat and Hofmann, Steve and Martell, José María and Toro, Tatiana (2019) 'Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition.' Advances in Calculus of Variations. ISSN 1864-8258 (Submitted)

Akman, Murat and Lewis, John and Vogel, Andrew (2017) 'σ-Finiteness of elliptic measures for quasilinear elliptic PDE in space.' Advances in Mathematics, 309. pp. 512-557. ISSN 0001-8708

Akman, Murat (2016) 'On the absolute continuity of p-harmonic measure and surface measure in Reifenberg flat domains.' Pacific Journal of Mathematics, 286 (1). pp. 25-37. ISSN 0030-8730

Akman, Murat and Lewis, John and Vogel, Andrew (2015) 'Hausdorff dimension and σ finiteness of p harmonic measures in space when p ≥ n.' Nonlinear Analysis: Theory, Methods and Applications, 129. pp. 198-216. ISSN 0362-546X

Akman, Murat (2014) 'On the dimension of a certain Borel measure in the plane.' Annales Academiae Scientiarum Fennicae. Mathematica, 39 (1). pp. 187-209. ISSN 1239-629X

Monograph

Akman, Murat and Lewis, John and Vogel, Andrew (2022) Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries. Working Paper. Communications in Partial Differential Equations. (In Press)

Book

Akman, Murat and Gong, Jasun and Hineman, Jay and Lewis, John and Vogel, Andrew (2022) The Brunn-Minkowski inequality and a Minkowski problem for nonlinear capacity. American Mathematical Society (AMS), vi+115-vi+115.

Thesis

Akman, Murat (2014) On the Hausdorff dimension of a certain measure arising from a positive weak solution to a divergence type PDE. PhD thesis, University of Kentucky.