40 citations · 112 across the 12 of their papers we have counts for
16 papers
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…
Transition probabilities for degenerate diffusions arising in population genetics
Charles L. Epstein, Camelia A. Pop
We provide a detailed description of the structure of the transition probabilities and of the hitting distributions of boundary components of a manifold with corners for a degenera…
Boundary estimates for a degenerate parabolic equation with partial Dirichlet boundary conditions
Charles L. Epstein, Camelia A. Pop
We study the boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted -norms for a…
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…
Harnack Inequalities for Degenerate Diffusions
Charles L. Epstein, Camelia A. Pop
We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion ope…