C0-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators

Camelia A. Pop

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 languageEnglish (US)
Pages (from-to)47-82
Number of pages36
JournalJournal of Functional Analysis
Volume272
Issue number1
DOIs
StatePublished - Jan 1 2017

Keywords

  • Anisotropic Hölder spaces
  • Degenerate diffusions
  • Degenerate elliptic operators
  • Kimura diffusions

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