- Arshak Petrosyan
- Professor of Mathematics
Address: Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Office: MATH 610 · Phone: +1 (765) 494-1932 · Fax: +1 (765) 494-0548
Email: arshak(at)math.purdue.edu
Research
Book(s)
- Regularity of free boundaries in obstacle-type problems, with H. Shahgholian and N. Uraltseva, Graduate Studies in Mathematics 136, American Mathematical Society, Providence, RI, 2012. x+221 pp.
Publications & Preprints
- [27] The two-phase fractional obstacle problem, with M. Allen and E. Lindgren, submitted
- [26] A two-phase problem with a lower-dimensional free boundary, with M. Allen, Interfaces Free Bound. 14 (2012), no. 3, 307–342.
- [25] Two-phase semilinear free boundary problem with a degenerate phase, with N. Matevosyan, Calc. Var. Partial Differential Equations 41 (2011), no 3–4, 397–411.
- [24] Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients, with N. Matevosyan, Comm. Pure Appl. Math. 64 (2011), no. 2., 271–311.
- [23] Optimal regularity in rooftop-like obstacle problem, with T. To, Comm. Partial Differential Equations 35 (2010), no. 7, 1292–1325.
- [22] Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem, with N. Garofalo, Invent. Math. 177 (2009), 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.