30 citations · 69 across the 22 of their papers we have counts for
11 papers · 1 filter
Solving the Scattering Problem for Open Wave-Guide Networks, III: Radiation Conditions and Uniqueness
Charles L. Epstein, Rafe Mazzeo
This paper continues the analysis of the scattering problem for a network of open wave-guides started in [arXiv:2302.04353, arXiv:2310.05816]. In this part we present explicit, phy…
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…
Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator
Charles L. Epstein, Jon Wilkening
We study the classical Kimura diffusion operator defined on the n-simplex, We give novel constructions for th…
Harnack Inequalities and Heat-kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology
Charles L. Epstein, Rafe Mazzeo
This paper continues the analysis, started in [2, 3], of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techni…
Regularity for the supercritical fractional Laplacian with drift
Charles L. Epstein, Camelia A. Pop
We consider the linear stationary equation defined by the fractional Laplacian with drift. In the supercritical case, that is the case when the dominant term is given by the drift…