79 citations · 125 across the 17 of their papers we have counts for
22 papers
Free boundary regularity for almost minimizers of the parabolic Signorini problem
Seongmin Jeon, Arshak Petrosyan
In this paper, we study the regularity of the "regular" part of the free boundary for almost minimizers in the parabolic Signorini problem with zero thin obstacle. This work is a c…
The obstacle problem for a higher order fractional Laplacian
Donatella Danielli, Alaa Haj Ali, Arshak Petrosyan
In this paper, we consider the obstacle problem for the fractional Laplace operator in the Euclidian space in the case where . As first observed in \…
Regularity of almost minimizers for the parabolic thin obstacle problem
Seongmin Jeon, Arshak Petrosyan
In this paper, we study almost minimizers for the parabolic thin obstacle (or Signorini) problem with zero obstacle. We establish their -regularity for every , as…
Nina Nikolaevna Uraltseva
Darya Apushkinskaya, Arshak Petrosyan, Henrik Shahgholian
Nina Uraltseva has made lasting contributions to mathematics with her pioneering work in various directions in analysis and PDEs and the development of elegant and sophisticated an…
Almost minimizers for the thin obstacle problem with variable coefficients
Seongmin Jeon, Arshak Petrosyan, Mariana Smit Vega Garcia
We study almost minimizers for the thin obstacle problem with variable Hölder continuous coefficients and zero thin obstacle and establish their regularity on the either…
The regular free boundary in the thin obstacle problem for degenerate parabolic equations
Agnid Banerjee, Donatella Danielli, Nicola Garofalo +1
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle probl…
Almost minimizers for the thin obstacle problem
Seongmin Jeon, Arshak Petrosyan
We consider Anzellotti-type almost minimizers for the thin obstacle (or Signorini) problem with zero thin obstacle and establish their regularity on the either side of th…
Almost minimizers for certain fractional variational problems
Seongmin Jeon, Arshak Petrosyan
In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension.…
The structure of the singular set in the thin obstacle problem for degenerate parabolic equations
Agnid Banerjee, Donatella Danielli, Nicola Garofalo +1
We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight for . Such problem arises as the local extension of the…
Obstacle problems for nonlocal operators: A brief overview
Donatella Danielli, Arshak Petrosyan, Camelia A. Pop
In this note, we give a brief overview of obstacle problems for nonlocal operators, focusing on the applications to financial mathematics. The class of nonlocal operators that we c…
Obstacle problems for nonlocal operators
Donatella Danielli, Arshak Petrosyan, Camelia A. Pop
We prove existence, uniqueness, and regularity of viscosity solutions to the stationary and evolution obstacle problems defined by a class of nonlocal operators that are not stable…
Boundedness and continuity of the time derivative in the parabolic Signorini problem
Arshak Petrosyan, Andrew Zeller
We prove the boundedness of the time derivative in the parabolic Signorini problem, as well as establish its Hölder continuity at regular free boundary points.
Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift
Nicola Garofalo, Arshak Petrosyan, Camelia A. Pop +1
We establish the -Hölder regularity of the regular free boundary in the stationary obstacle problem defined by the fractional Laplace operator with drift in the subcritica…
Singular Perturbation Problem in Boundary/Fractional Combustion
Arshak Petrosyan, Wenhui Shi, Yannick Sire
Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction-diffusion equation, where the rea…
An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients
Nicola Garofalo, Arshak Petrosyan, Mariana Smit Vega Garcia
In this paper we establish the regularity of the regular part of the free boundary in the Signorini problem for elliptic operators with variable Lipschitz coefficients. T…
Contact of a thin free boundary with a fixed one in the Signorini problem
Norayr Matevosyan, Arshak Petrosyan
We study the Signorini problem near a fixed boundary, where the solution is "clamped down" or "glued." We show that in general the solutions are at least regular and that…
Higher regularity of the free boundary in the elliptic Signorini problem
Herbert Koch, Arshak Petrosyan, Wenhui Shi
In this paper we study the higher regularity of the free boundary for the elliptic Signorini problem. By using a partial hodograph-Legendre transformation we show that the regular…
Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift
Arshak Petrosyan, Camelia A. Pop
We prove existence, uniqueness and optimal regularity of solutions to the stationary obstacle problem defined by the fractional Laplacian operator with drift, in the subcritical re…
Parabolic Boundary Harnack Principles in Domains with Thin Lipschitz Complement
Arshak Petrosyan, Wenhui shi
We prove forward and backward parabolic boundary Harnack principles for nonnegative solutions of the heat equation in the complements of thin parabolic Lipschitz sets given as subg…
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
Donatella Danielli, Nicola Garofalo, Arshak Petrosyan +1
We give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This includes the proof of the optimal re…
The two-phase fractional obstacle problem
Mark Allen, Erik Lindgren, Arshak Petrosyan
We study minimizers of the functional for . The problem arises in connection with heat…
Some New Monotonicity Formulas and the Singular Set in the Lower Dimensional Obstacle Problem
Nicola Garofalo, Arshak Petrosyan
We construct two new one-parameter families of monotonicity formulas to study the free boundary points in the lower dimensional obstacle problem. The first one is a family of Weiss…