Abstract
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.
Original language | English (US) |
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Pages (from-to) | 47-82 |
Number of pages | 36 |
Journal | Journal of Functional Analysis |
Volume | 272 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2017 |
Bibliographical note
Publisher Copyright:© 2016 Elsevier Inc.
Keywords
- Anisotropic Hölder spaces
- Degenerate diffusions
- Degenerate elliptic operators
- Kimura diffusions