On a generalization of the Neumann problem for the Laplace equation
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DOI: 10.1002/mana.201800219
Abstract: We investigate solvability of a fractional analogue of the Neumann problem for the Laplace equation. As a boundary operator we consider operators of fractional differentiation in the Hadamard sense. The problem is solved by reduction… read more here.
Keywords: neumann problem; laplace equation; problem; equation ... See more keywords
Basis Property of the System of Root Functions of the Oblique Derivative Problem for the Laplace Operator in a Disk
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DOI: 10.1134/s0012266119100100
Abstract: We study the spectral oblique derivative problem for the Laplace operator in a disk D. The asymptotic properties of the eigenvalues are established, and the basis property with parentheses in the space L2(D) is proved… read more here.
Keywords: operator disk; laplace operator; oblique derivative; problem laplace ... See more keywords
Homogenization of the boundary value problem for the Laplace operator in a domain perforated along (n – 1)-dimensional manifold with nonlinear Robin type boundary condition on the boundary of arbitrary shaped holes: Critical case
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DOI: 10.1134/s1064562417060229
Abstract: The asymptotic behavior of the solution to the boundary value problem for the Laplace operator in a domain perforated along an (n − 1)-dimensional manifold is studied. A nonlinear Robin-type condition is assumed to hold… read more here.
Keywords: domain perforated; value problem; problem laplace; boundary value ... See more keywords
An Analog of the Neumann Problem for the 1-Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability
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DOI: 10.1515/agms-2018-0001
Abstract: Abstract We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincaré inequality. We show that… read more here.
Keywords: regularity; problem laplace; neumann problem; stability ... See more keywords