We propose the L 2-version of Laplacian with respect to a measure on the (infinite-dimensional) Riemannian manifold. The Dirichlet problem for equations with the introduced Laplacian is solved in a part of the Riemannian manifold of a certain class.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 11, pp. 1443–1449, November, 2016.
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Bogdanskii, Y.V., Potapenko, A.Y. Laplacian with Respect to a Measure on the Riemannian Manifold and the Dirichlet Problem. II. Ukr Math J 68, 1665–1672 (2017). https://doi.org/10.1007/s11253-017-1319-5
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DOI: https://doi.org/10.1007/s11253-017-1319-5