Laplacian with respect to a measure on a Hilbert space and an \(L_2\)-version of the Dirichlet problem for the Poisson equation. (English. Russian original) Zbl 1260.35021

Ukr. Math. J. 63, No. 9, 1336-1348 (2012); translation from Ukr. Mat. Zh. 63, No. 9, 1169-1178 (2011).
In this article, a new version of the Laplacian for functions defined on a Hilbert space with measure is proposed. Additionally, the author investigates uniqueness of the Poisson equation with Dirichlet boundary condition as an application.


35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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