Address: Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Phone: +1 (765) 494-1932 Fax: +1 (765) 494-0548
Email: arshak(at)math.purdue.edu
Research
Publications & Preprints
- [25] Two-phase semilinear free boundary problem with a degenerate phase, with N. Matevosyan, submitted.
- [24] Optimal regularity in rooftop-like obstacle problem, with T. To, submitted.
- [23] Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients, with N. Matevosyan, submitted.
- [22] Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem, with N. Garofalo, Invent. Math. 177, no. 2, 415–461.
- [21] Nonuniqueness in a free boundary problem from combustion, with N.K. Yip, J. Geom. Anal. 18 (2008), 1098–1126.
- [20] Regularity of the free boundary in a two-phase semilinear problem in two dimensions, with E. Lindgren, Indiana Univ. Math. J. 57 (2008), 3397–3418.
- [19] A parabolic almost monotonicity formula, with A. Edquist, Math. Ann. 341 (2008), no. 2, 429–454.
- [18] Parabolic obstacle problems applied to finance: free-boundary-regularity approach, with H. Shahgholian, appendix by T. Arnarson, Recent Developments in Nonlinear Partial Differential Equations, Contemporary Matematics 439 (2007), 117–133.
- [17] On the full regularity of the free boundary in a class of variational problems, Proc. Amer. Math. Soc. 136 (2008), no. 8, 2763–2769.
- [16] Geometric and energetic criteria for the free boundary regularity in an obstacle-type problem, with H. Shahgholian, Amer. J. Math. 129 (2007), no. 6, 1659–1688.
- [15] The sub-elliptic obstacle problem: $C^{1,\alpha}$ regularity of the free boundary in Carnot groups of step two, with D. Danielli and N. Garofalo, Adv. Math. 211 (2007), no. 2, 485–516.
- [14] Large time geometric properties of solutions of the evolution p-Laplacian equation, with K. Lee and J.L. Vazquez, J. Differential Equations 229 (2006), no. 2, 389–411.