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

DOI10.1007/s11253-012-0582-8zbMath1260.35021OpenAlexW2009648055MaRDI QIDQ1759980

Yu. V. Bogdanskij

Publication date: 23 November 2012

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

Full work available at URL: https://doi.org/10.1007/s11253-012-0582-8

zbMATH Keywords

Hilbert spacePoisson equationLaplacian

Mathematics Subject Classification ID

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

Related Items (9)

Uniform continuity and Brézis-Lieb-type splitting for superposition operators in Sobolev space ⋮ 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 ⋮ The Dirichlet problem with Laplacian with respect to a measure in the Hilbert space ⋮ Infinite-dimensional version of the Friedrichs inequality

Cites Work

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• Limit laws for norms of IID samples with Weibull tails
• The Cauchy problem for parabolic equations with essentially infinite- dimensional elliptic operators
• Differentiable measures and the Malliavin calculus
• Potential theory on Hilbert space
• EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES
• A QUANTUM APPROACH TO LAPLACE OPERATORS

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