Publications and preprints:

  1. Two-phase semilinear free boundary problem with a degenerate phase, Calculus of Variations and PDE's, to appear, with A. Petrosyan.
  2. Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients, Communications On Pure & Applied Mathematics, 64 (2011), no. 2, 271--311, with A. Petrosyan.
  3. A level set based shape optimization method for an elliptic obstacle problem, M3 AS: Mathematical Models and Methods in Applied Sciences, to appear, with M. Burger and M.-T. Wolfram.
  4. On a parabolic free boundary equation modeling price formation, M3 AS: Mathematical Models and Methods in Applied Sciences, vol 19, 10(2009), 1929--1957, with P.A. Markowich, J.-F. Pietschmann, and M.-T. Wolfram.
  5. Regularity of a free boundary in parabolic problem without sign restriction, Indiana Univ. Math. J., 58, No. 2 (2009), with D.E. Apushkinskaya and N.N. Uraltseva.
  6. On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem, Ark. Mat. 44 (2006), no. 1, 1—15, with J. Andersson, H. Mikayelyan
  7. Tangential touch between free and fixed boundaries in a problem from superconductivity. Comm. Partial Differential Equations 30 (2005), no. 7-9, 1205--1216.
  8. Behavior of the free boundary near contact points with the fixed boundary for nonlinear elliptic equations. Monatsh. Math. 142 (2004), no. 1-2, 17—25, with Markowich, Peter A.
  9. Three spheres theorem for harmonic functions. J. Contemp. Math. Anal. 34 (1999), no. 3, 1--9 (2000); translated from Izv. Nats. Akad. Nauk Armenii Mat. 34 (1999), no. 3, 5--13 (2001), with Arakelian, N. U.


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