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

  • Yu. V. Bogdanskii
  • A. Yu. Potapenko


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.
How to Cite
BogdanskiiY. V., and PotapenkoA. Y. “Laplacian With Respect to Measure on a Riemannian Manifold and Dirichlet Problem. I”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 7, July 2016, pp. 897-0,
Research articles