2014/06/03 by Camelia A. Pop, Pop, Camelia A.
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #math.AP
paper · pdf · doi:10.48550/arxiv.1406.0742
arxiv created 2014/06/03 · openalex publication_date 2014/06/03 · arxiv updated 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kimura diffusions serve as a stochastic model for the evolution of gene frequencies in population genetics. Their infinitesimal generator is an elliptic differential operator whose second-order coefficients matrix degenerates on the boundary of the domain. In this article, we consider the inhomogeneous initial-value problem defined by generators of Kimura diffusions, and we establish C0-estimates, which allows us to prove that solutions to the inhomogeneous initial-value problem are smooth up to the boundary of the domain where the operator degenerates, even when the initial data is only assumed to be continuous.