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)

GSM-136
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.
  • [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.
  • [13] Full regularity of the free boundary in a Bernoulli-type problem in two dimensions, with D. Danielli, Math. Res. Lett. 13 (2006), no. 4, 667–681.
  • [12] Density estimates for a degenerate/singularphase-transition model, with E. Valdinoci, SIAM J. Math. Anal. 36 (2005), no. 4, 1057–1079.
  • [11] Geometric properties of Bernoulli-type minimizers, with E. Valdinoci, Interfaces Free Bound. 7 (2005), no. 1, 55–77.
  • [10] A minimum problem with free boundary for a degenerate quasilinear operator, with D. Danielli, Calc. Var. Partial Differential Equations 23 (2005), no. 1, 97–124.
  • [9] Regularity of a free boundary in parabolic potential theory, with L. Caffarelli and H. Shahgholian, J. Amer. Math. Soc. 17 (2004), 827–869.
  • [8] A singular perturbation problem for p-Laplace operator, with D. Danielli and H. Shahgholian, Indiana Univ. Math. J. 52 (2003), 457–476.
  • [7] On existence and uniqueness in a free boundary problem from combustion, Comm. Partial Differential Equations 27 (2002), no. 3-4, 763–789.
  • [6] A free boundary problem for $\infty$-Laplace equation, with J. Manfredi and H. Shahgholian, Calc. Var. Partial Differential Equations 14 (2002), no. 3, 359–384.
  • [5] Propagation of smallness and the uniqueness of solutions to some elliptic equations in the plane, J. Math. Anal. Appl. 267 (2002), no. 2, 460–470.
  • [4] Convexity and uniqueness in a free boundary problem arising in combustion theory, Rev. Mat. Iberoamericana 17 (2001), no. 3, 421–431.
  • [3] On the porosity of free boundaries in degenerate variational inequalities, with L. Karp, T. Kilpeläinen and H. Shahgholian, J. Differential Equations 164 (2000), no. 1, 110–117.
  • [2] The slice classification of categories of coalgebras for comonads, with S. Dalalyan, Algebra Universalis 41 (1999), no. 3, 177–185.
  • [1] Some extremal problems for analytic functions, Complex Variables Theory Appl. 39 (1999), no. 2, 137–159.
  • [PhD Thesis] Convex configurations in free boundary problems, Royal Institute of Technology, Stockholm, 2000.