Abstract
We prove that the Dirichlet problem for the Poisson equation with an elliptic operator of the form(Lu)(x)=j (x)(u″(x)) vanishing on cylindrical functions is solvable for a special class of domains in an infinite-dimensional Hilbert space.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 803–808, July, 1994.
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Bogdanskii, Y.V. Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator. Ukr Math J 46, 878–884 (1994). https://doi.org/10.1007/BF01056664
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DOI: https://doi.org/10.1007/BF01056664