2017
Том 69
№ 7

All Issues

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

Bogdanskii Yu. V., Potapenko A. Yu.


Abstract

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

Citation Example: Bogdanskii Yu. V., Potapenko A. Yu. Laplacian with respect to the measure on a Riemannian manifold and the Dirichlet problem. II // Ukr. Mat. Zh. - 2016. - 68, № 11. - pp. 1443-1449.