Laplacian with respect to a measure on a Riemannian manifold and the Dirichlet problem. I

DOI10.1007/s11253-016-1274-6zbMath1499.58016OpenAlexW2558028524WikidataQ115380340 ScholiaQ115380340MaRDI QIDQ1729512

A. Yu. Potapenko, Yu. V. Bogdanskij

Publication date: 27 February 2019

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

Full work available at URL: https://doi.org/10.1007/s11253-016-1274-6

zbMATH Keywords

Dirichlet problemmeasureLaplacianinfinite-dimensional Riemannian manifold

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) PDEs on manifolds (35R01)

Related Items

Divergence theorem in the \(L_2\)-version. Application to the Dirichlet problem, Divergence of multivector fields on infinite-dimensional manifolds, Laplacian with respect to a measure on the Riemannian manifold and the Dirichlet problem. II, Lévy Laplacian on manifold and Yang-Mills heat flow, Stokes formula for Banach manifolds, Infinite-dimensional version of the Friedrichs inequality

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