On the Solution of the Dirichlet Problem for the Two-Dimensional Laplace Equation

DOI10.2307/2160526zbMath0795.35020OpenAlexW4252886836MaRDI QIDQ4275652

Christian Constanda

Publication date: 14 September 1994

Full work available at URL: https://doi.org/10.2307/2160526

zbMATH Keywords

Dirichlet problemtwo-dimensional Laplace equationmodified single layer potentiallogarithmic capacity of the boundary curve

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

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An indirect BIE free of degenerate scales ⋮ Boundary value problems associated with Newton's law of cooling ⋮ Singular boundary method: a review and computer implementation aspects ⋮ Revisit of the indirect boundary element method: necessary and sufficient formulation ⋮ Formulation of the MFS for the two-dimensional Laplace equation with an added constant and constraint ⋮ Dynamics and stability of air bubbles in a porous medium ⋮ Unnamed Item ⋮ Revisit of a degenerate scale: a semi-circular disc ⋮ Analytical derivation and numerical experiments of degenerate scale for an ellipse in BEM ⋮ Linkage between the unit logarithmic capacity in the theory of complex variables and the degenerate scale in the BEM/BIEMs

Cites Work

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• Symmetrizing Kernels and the Integral Equations of First Kind of Classical Potential Theory
• Solution of Boundary Value Problems by Integral Equations of the First Kind

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