Dirichlet problem for the Poisson equation with an essentially infinite-dimensional elliptic operator - Bogdanskii, Yu. V. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
In a special class of domains in an infinite-dimensional Hilbert space, the solvability of 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 proved.