2017
Том 69
№ 9

All Issues

Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator

Bogdanskii Yu. V.

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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.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 7, pp 878-884.

Citation Example: Bogdanskii Yu. V. Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator // Ukr. Mat. Zh. - 1994. - 46, № 7. - pp. 803–808.

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