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Laplacian with respect to a measure on a Hilbert space and an L 2-version of the Dirichlet problem for the Poisson equation

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Ukrainian Mathematical Journal Aims and scope

We propose a version of the Laplace operator for functions on a Hilbert space with measure. In terms of this operator, we investigate the Dirichlet problem for the Poisson equation.

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Authors and Affiliations

  1. Institute of Applied Systems Analysis, “Kyiv Polytechnic Institute” National Technical University, Kyiv, Ukraine

    Yu. V. Bogdanskii

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  1. Yu. V. Bogdanskii
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1169–1178, September, 2011.

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Bogdanskii, Y.V. Laplacian with respect to a measure on a Hilbert space and an L 2-version of the Dirichlet problem for the Poisson equation. Ukr Math J 63, 1336–1348 (2012). https://doi.org/10.1007/s11253-012-0582-8

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  • DOI: https://doi.org/10.1007/s11253-012-0582-8

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