Displaying similar documents to “The multiple layer potential for the biharmonic equation in n variables”

The simple layer potential for the biharmonic equation in n variables

Alberto Cialdea (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A theory of the «simple layer potential» for the classical biharmonic problem in R n is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with n scalar components into a vector whose components are n differential forms of degree one.

The third boundary value problem in potential theory for domains with a piecewise smooth boundary

Dagmar Medková (1997)

Czechoslovak Mathematical Journal

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The paper investigates the third boundary value problem ∂ u ∂ n + λ u = μ for the Laplace equation by the means of the potential theory. The solution is sought in the form of the Newtonian potential (1), (2), where ν is the unknown signed measure on the boundary. The boundary condition (4) is weakly characterized by a signed measure T ν . Denote by T ν → T ν the corresponding operator on the space of signed measures on the boundary of the investigated domain G . If there is α ≠ 0 such that the essential spectral radius...

Solution of the Dirichlet problem for the Laplace equation

Dagmar Medková (1999)

Applications of Mathematics

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For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.