2017
Том 69
№ 6

All Issues

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

Bogdanskii Yu. V., Potapenko A. Yu.


Abstract

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.

Citation Example: Bogdanskii Yu. V., Potapenko A. Yu. Laplacian with respect to measure on a Riemannian manifold and Dirichlet problem. I // Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 897-907.