The Dirichlet problem with Laplacian with respect to a measure in the Hilbert space

DOI10.1007/s11253-014-0976-xzbMath1432.35234OpenAlexW2048120653MaRDI QIDQ2260850

Ya. Yu. Sanzharevskii, Yu. V. Bogdanskij

Publication date: 12 March 2015

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-014-0976-x

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) PDEs with measure (35R06)

Related Items (9)

Transitivity of the surface measures on Banach manifolds with uniform structures ⋮ Laplacian generated by the Gaussian measure and ergodic theorem ⋮ Divergence theorem in the \(L_2\)-version. Application to the Dirichlet problem ⋮ Boundary trace operator in a domain of Hilbert space and the characteristic property of its kernel ⋮ Laplacian with respect to a measure on the Riemannian manifold and the Dirichlet problem. II ⋮ Maximum principle for the Laplacian with respect to a measure in a domain of the Hilbert space ⋮ Laplacian with respect to a measure on a Riemannian manifold and the Dirichlet problem. I ⋮ Infinite-dimensional version of the Friedrichs inequality ⋮ Surface measures on Banach manifolds with uniform structure

Cites Work

• Differentiable measures and the Malliavin calculus
• Laplacian with respect to a measure on a Hilbert space and an \(L_2\)-version of the Dirichlet problem for the Poisson equation
• Banach manifolds with bounded structure and the Gauss-Ostrogradskii formula

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