We propose an L 2-version of the Laplacian with respect to a measure on the infinite-dimensional Riemannian manifold. The Dirichlet problem for equations with the proposed Laplacian is solved in a region of the Riemannian manifold from a certain class.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 7, pp. 897–907, July, 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. I. Ukr Math J 68, 1021–1033 (2016). https://doi.org/10.1007/s11253-016-1274-6
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DOI: https://doi.org/10.1007/s11253-016-1274-6