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

Bogdanskii, Yu. V.

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.

Reviewer: Andreas Kleefeld (Cottbus)

MSC:

35J05

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

Keywords:

Laplacian; Hilbert space; Poisson equation

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