电邮这篇文章 $L_p$-approximations for solutions of parabolic differential equations on manifolds
- 作者: Smirnova A.S.1
-
隶属关系:
- Higher School of Economics
- 期: 卷 24, 编号 3 (2022)
- 页面: 297-303
- 栏目: Mathematics
- ##submission.datePublished##: 24.08.2022
- URL: https://journals.rcsi.science/2079-6900/article/view/366177
- DOI: https://doi.org/10.15507/2079-6900.24.202203.297-303
- ID: 366177
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The paper considers the Cauchy problem for a parabolic partial differential equation in a Riemannian manifold of bounded geometry. A formula is given that expresses arbitrarily accurate (in the $L_p$-norm) approximations to the solution of the Cauchy problem in terms of parameters - the coefficients of the equation and the initial condition. The manifold is not assumed to be compact, which creates significant technical difficulties - for example, integrals over the manifold become improper in the case when the manifold has an infinite volume. The presented approximation method is based on Chernoff theorem on approximation of operator semigroups.
作者简介
Anna Smirnova
Higher School of Economics
编辑信件的主要联系方式.
Email: smirnovaas@hse.ru
ORCID iD: 0000-0003-4172-2811
Postgraduate Student, Department of Fundamental Mathematics
俄罗斯联邦, 25/12 B. Pecherskaya St., Nizhny Novgorod 603150, Russia参考
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