# Dr. Arshak Petrosyan

**Professor of Mathematics, Associate Department Head**

- 765 49-41932

- MATH 836

###### Research Interest(s):

Partial Differential Equations

#### Publications listed in MathSciNet

[36] | Nicola Garofalo, Arshak Petrosyan, Camelia A. Pop, and Mariana Smit Vega Garcia. Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift. Ann. Inst. H. Poincaré Anal. Non Linéaire , 34(3):533-570, 2017. [ DOI | http ] |

[35] | Nicola Garofalo, Arshak Petrosyan, and Mariana Smit Vega Garcia. An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients. J. Math. Pures Appl. (9) , 105(6):745-787, 2016. [ DOI | http ] |

[34] | Arshak Petrosyan, Wenhui Shi, and Yannick Sire. Singular perturbation problem in boundary/fractional combustion. Nonlinear Anal. , 138:346-368, 2016. [ DOI | http ] |

[33] | N. Matevosyan and A. Petrosyan. Contact of a thin free boundary with a fixed one in the Signorini problem. Algebra i Analiz , 27(3):183-201, 2015. |

[32] | Herbert Koch, Arshak Petrosyan, and Wenhui Shi. Higher regularity of the free boundary in the elliptic Signorini problem. Nonlinear Anal. , 126:3-44, 2015. [ DOI | http ] |

[31] | Mark Allen, Erik Lindgren, and Arshak Petrosyan. The Two-Phase Fractional Obstacle Problem. SIAM J. Math. Anal. , 47(3):1879-1905, 2015. [ DOI | http ] |

[30] | Arshak Petrosyan and Camelia A. Pop. Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift. J. Funct. Anal. , 268(2):417-472, 2015. [ DOI | http ] |

[29] | Arshak Petrosyan and Wenhui Shi. Parabolic boundary Harnack principles in domains with thin Lipschitz complement. Anal. PDE , 7(6):1421-1463, 2014. [ DOI | http ] |

[28] | Mark Allen and Arshak Petrosyan. A two-phase problem with a lower-dimensional free boundary. Interfaces Free Bound. , 14(3):307-342, 2012. [ DOI | http ] |

[27] | Arshak Petrosyan, Henrik Shahgholian, and Nina Uraltseva. Regularity of free boundaries in obstacle-type problems , volume 136 of Graduate Studies in Mathematics . American Mathematical Society, Providence, RI, 2012. |

[26] | Norayr Matevosyan and Arshak Petrosyan. Two-phase semilinear free boundary problem with a degenerate phase. Calc. Var. Partial Differential Equations , 41(3-4):397-411, 2011. [ DOI | http ] |

[25] | Norayr Matevosyan and Arshak Petrosyan. Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients. Comm. Pure Appl. Math. , 64(2):271-311, 2011. [ DOI | http ] |

[24] | Arshak Petrosyan and Tung To. Optimal regularity in rooftop-like obstacle problem. Comm. Partial Differential Equations , 35(7):1292-1325, 2010. [ DOI | http ] |

[23] | Nicola Garofalo and Arshak Petrosyan. Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem. Invent. Math. , 177(2):415-461, 2009. [ DOI | http ] |

[22] | Erik Lindgren and Arshak Petrosyan. Regularity of the free boundary in a two-phase semilinear problem in two dimensions. Indiana Univ. Math. J. , 57(7):3397-3417, 2008. [ DOI | http ] |

[21] | Arshak Petrosyan and Nung Kwan Yip. Nonuniqueness in a free boundary problem from combustion. J. Geom. Anal. , 18(4):1098-1126, 2008. [ DOI | http ] |

[20] | Arshak Petrosyan. On the full regularity of the free boundary in a class of variational problems. Proc. Amer. Math. Soc. , 136(8):2763-2769, 2008. [ DOI | http ] |

[19] | Anders Edquist and Arshak Petrosyan. A parabolic almost monotonicity formula. Math. Ann. , 341(2):429-454, 2008. [ DOI | http ] |

[18] | Arshak Petrosyan and Henrik Shahgholian. Geometric and energetic criteria for the free boundary regularity in an obstacle-type problem. Amer. J. Math. , 129(6):1659-1688, 2007. [ DOI | http ] |

[17] | Arshak Petrosyan and Henrik Shahgholian. Parabolic obstacle problems applied to finance. In Recent developments in nonlinear partial differential equations , volume 439 of Contemp. Math. , pages 117-133. Amer. Math. Soc., Providence, RI, 2007. [ DOI | http ] |

[16] | Donatella Danielli, Nicola Garofalo, and Arshak Petrosyan. The sub-elliptic obstacle problem: C 1,α regularity of the free boundary in Carnot groups of step two. Adv. Math. , 211(2):485-516, 2007. [ DOI | http ] |

[15] | Ki-ahm Lee, Arshak Petrosyan, and Juan Luis Vázquez. Large-time geometric properties of solutions of the evolution p -Laplacian equation. J. Differential Equations , 229(2):389-411, 2006. [ DOI | http ] |

[14] | Donatella Danielli and Arshak Petrosyan. Full regularity of the free boundary in a Bernoulli-type problem in two dimensions. Math. Res. Lett. , 13(4):667-681, 2006. [ DOI | http ] |

[13] | Arshak Petrosyan and Enrico Valdinoci. Density estimates for a degenerate/singular phase-transition model. SIAM J. Math. Anal. , 36(4):1057-1079 (electronic), 2005. [ DOI | http ] |

[12] | Donatella Danielli and Arshak Petrosyan. A minimum problem with free boundary for a degenerate quasilinear operator. Calc. Var. Partial Differential Equations , 23(1):97-124, 2005. [ DOI | http ] |

[11] | Arshak Petrosyan and Enrico Valdinoci. Geometric properties of Bernoulli-type minimizers. Interfaces Free Bound. , 7(1):55-77, 2005. [ DOI | http ] |

[10] | Luis Caffarelli, Arshak Petrosyan, and Henrik Shahgholian. Regularity of a free boundary in parabolic potential theory. J. Amer. Math. Soc. , 17(4):827-869, 2004. [ DOI | http ] |

[9] | D. Danielli, A. Petrosyan, and H. Shahgholian. A singular perturbation problem for the p -Laplace operator. Indiana Univ. Math. J. , 52(2):457-476, 2003. [ DOI | http ] |

[8] | Arshak Petrosyan. On existence and uniqueness in a free boundary problem from combustion. Comm. Partial Differential Equations , 27(3-4):763-789, 2002. [ DOI | http ] |

[7] | Juan Manfredi, Arshak Petrosyan, and Henrik Shahgholian. A free boundary problem for -Laplace equation. Calc. Var. Partial Differential Equations , 14(3):359-384, 2002. [ DOI | http ] |

[6] | Arshak Petrosyan. Propagation of smallness and the uniqueness of solutions to some elliptic equations in the plane. J. Math. Anal. Appl. , 267(2):460-470, 2002. [ DOI | http ] |

[5] | Arshak Petrosyan. Convexity and uniqueness in a free boundary problem arising in combustion theory. Rev. Mat. Iberoamericana , 17(3):421-431, 2001. [ DOI | http ] |

[4] | Arshak Petrosyan. Convex configurations in free boundary problems . Thesis (Fil.Dr.)-Kungliga Tekniska Högskolan (Sweden), 2000. [ http ] |

[3] | L. Karp, T. Kilpeläinen, A. Petrosyan, and H. Shahgholian. On the porosity of free boundaries in degenerate variational inequalities. J. Differential Equations , 164(1):110-117, 2000. [ DOI | http ] |

[2] | Arshak Petrosyan. Some extremal problems for analytic functions. Complex Variables Theory Appl. , 39(2):137-159, 1999. |

[1] | S. Dalalyan and A. Petrosyan. The slice classification of categories of coalgebras for comonads. Algebra Universalis , 41(3):177-185, 1999. [ DOI | http ] |