2019
Том 71
№ 11

All Issues

Potapenko A. Yu.

Articles: 2
Article (Russian)

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

Bogdanskii Yu. V., Potapenko A. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 11. - pp. 1443-1449

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.

Article (Russian)

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

Bogdanskii Yu. V., Potapenko A. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 897-907

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.