Laplacian with respect to measure on a Riemannian manifold and Dirichlet problem. I

We propose an $L^2$ -version of the Laplacian with respect to measure on an infinite-dimensional Riemannian manifold. The Dirichlet problem for equations with proposed Laplacian is solved in the region of a Rimannian manifold from a certain class.

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Bibliographic Details
Date:2016
Main Authors: Bogdanskii, Yu. V., Potapenko, A. Yu., Богданский, Ю. В., Потапенко, А. Ю.
Format: Article
Language:Russian
Published: Institute of Mathematics, NAS of Ukraine 2016
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/1889
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal