Welcome
I am currently a postdoc researcher at RWTH Aachen. I have obtained my Ph.D. in mathematics at Purdue University in August 2013 under the supervision of Arshak Petrosyan. Afterwards, I was a postdoc at the Hausdorff Center for Mathematics at Bonn, CMUC at University of Coimbra, and Institute of Applied Mathematics at Universität Heidelberg. From 2019-2024 I was a lecturer at Monash University. For more details, please see my CV.
Address:
RWTH Aachen University
Lehrstuhl für Angewandte Analysis
Pontdriesch 14-16, Raum 211
52062 Aachen
Research interests:
free boundary problems, calculus of variations
Preprints:
Two dimensional jet flows for compressible Euler system with non-zero vorticity. (with Y. Li, L. Tang and C. Xie), submitted.
Optimal regularity for the variable coefficients parabolic Signorini problem (with V. Arya), submitted
Publications:
Second order expansion for the nonlocal perimeter functional (with H. Knüpfer), Commun. Math. Phys. 398, 1371–1402 (2023).
Higher regularity for the Signorini problem for the homogeneous, isotropic Lamé system. (with A. Rüland), Nonlinear Analysis, Theory, Methods and Applications. Volume 217 (2022).
Γ-limit for two-dimensional charged magnetic zigzag domain walls. (with H. Knüpfer), Arch. Ration. Mech. Anal. 239, 1875-1923, (2021).
An epiperimetric inequality approach to the parabolic Signorini problem. Discrete Contin. Dyn. Syst. A, 40(3):1813–1846, (2020).
The gradient flow of the potential energy on the space of arcs. (with D. Vorotnikov), Calc. Var. Partial Differential Equations 58:2 (2019)
Uniformly compressing mean curvature flow. (with D. Vorotnikov), Geom. Anal., vol. 29 (2019), no. 4, pp. 3055–3097
Optimal regularity for the thin obstacle problem with $C^{0,\alpha}$ coefficients. (with A. Rüland), Calc. Var. Partial Differential Equations 56:129 (2017), no. 5
Higher regularity for the fractional thin obstacle problem. (with H. Koch, A. Rüland), New York J. Math., vol. 25 (2019), pp. 745–838
The variable coefficient thin obstacle problem: higher regularity. (with H. Koch, A. Rüland), Adv. Differential Equations. 22 (2017), no. 11-12, 793-866
The variable coefficient thin obstacle problem: optimal regularity and regularity of the regular free boundary. (with H. Koch, A. Rüland), Annales de l'Institut Henri Poincare (C) Non Linear Analysis. 34 (2017), no. 4, 845-897
The variable coefficient thin obstacle problem: Carleman inequalities. (with H. Koch, A. Rüland), Advances in Mathematics. 301 (2016), no. 1, 820-866
The two-phase parabolic Signorini problem. (with M. Allen), Indiana Univ. Math. J. 65 (2016), 727-741
Singular perturbation problem in boundary/fractional combustion. (with A. Petrosyan, Y. Sire), Nonlinear Anal. 138 (2016), 346-368
Higher regularity of the free boundary in the elliptic Signorini problem. (with H. Koch, A. Petrosyan), Nonlinear Anal. 126 (2015), 3-44
Parabolic boundary Harnack principle in domains with thin Lipschitz complement. (with A. Petrosyan), Anal. PDE 7 (2014), no. 6, 1421--1463