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

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• 作者：Camelia A. Pop ^{capop@umn.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 35J70 ; secondary ; 60J60
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：272
• 期：1
• 页码：47-82
• 全文大小：611 K

文摘

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$C^0$-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.