Divergence theorem in the \(L_2\)-version. Application to the Dirichlet problem

DOI10.1007/s11253-018-1527-7zbMath1499.26042OpenAlexW2900825450MaRDI QIDQ2417270

Yu. V. Bogdanskij

Publication date: 12 June 2019

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

Full work available at URL: https://doi.org/10.1007/s11253-018-1527-7

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Differentiability questions for infinite-dimensional manifolds (58B10) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20) Green's functions for elliptic equations (35J08)

Related Items (1)

Stokes formula for Banach manifolds

Cites Work

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