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Ukrainian Mathematical Journal

, Volume 66, Issue 6, pp 818–826 | Cite as

The Dirichlet Problem with Laplacian with Respect to a Measure in the Hilbert Space

  • Yu. V. Bogdanskii
  • Ya. Yu. Sanzharevskii
Article

We study the Dirichlet problem for a specified class of elliptic equations in a region of the Hilbert space consistent with a given Borel measure.

Keywords

Hilbert Space Weak Solution Dirichlet Problem Borel Measure Gaussian Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Yu. V. Bogdanskii, “Laplacian with respect to a measure on a Hilbert space and the L2-version of the Dirichlet problem for the Poisson equation,” Ukr. Mat. Zh., 63, No. 9, 1169–1178 (2011); English translation: Ukr. Math. J., 63, No. 9, 1339–1348 (2012).Google Scholar
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    Yu. V. Bogdanskii, “Banach manifolds with bounded structure and the Gauss–Ostrogradskii formula,” Ukr. Mat. Zh., 64, No. 10, 1299–1313 (2012); English translation: Ukr. Math. J., 64, No. 10, 1475–1494 (2013).Google Scholar
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    V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).Google Scholar
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    V. I. Bogachev, Foundations of Measure Theory [in Russian], Vol. 1, RKhD, Moscow (2006).Google Scholar
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    V. I. Bogachev, Differentiable Measures and the Malliavin Calculus [in Russian], RKhD, Moscow (2008).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yu. V. Bogdanskii
    • 1
  • Ya. Yu. Sanzharevskii
    • 1
  1. 1.Institute of Applied System Analysis of the “Kiev Polytechnic Institute” Ukrainian National Technical UniversityKievUkraine

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