# Welcome

I am currently a lecturer at Monash University. 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. For more details, please see my CV.

**Address**:

9 Rainforest Walk, Level 4

Monash University

Clayton 3168, VIC

Australia

## Research interests:

Research interests:

free boundary problems, calculus of variations

## Preprints:

Preprints:

- Γ-limit for two-dimensional charged magnetic zigzag domain walls.
*(with H. Knüpfer), submitted.* - Two dimensional jet flows for compressible Euler system with non-zero vorticity.
*(with L. Tang and C. Xie), submitted.*

## Publications:

Publications:

- An epiperimetric inequality approach to the parabolic Signorini problem.
*,*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*), - 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