Layer potentials on boundaries with corners and edges

Thomas S. Angell; Ralph Ellis Kleinman; Josef Král

Displaying similar documents to “Layer potentials on boundaries with corners and edges”

Double layer potentials on boundaries with corners and edges

Thomas S. Angell, Ralph Ellis Kleinman, Josef Král (1986)

Commentationes Mathematicae Universitatis Carolinae

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Some examples concerning applicability of the Fredholm-Radon method in potential theory

Josef Král, Wolfgang L. Wendland (1986)

Aplikace matematiky

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Simple examples of bounded domains $D \subset 𝐑^{3}$ are considered for which the presence of peculiar corners and edges in the boundary $δ D$ causes that the double layer potential operator acting on the space $𝒮 (δ D)$ of all continuous functions on $δ D$ can for no value of the parameter $α$ be approximated (in the sub-norm) by means of operators of the form $α I + T$ (where $I$ is the identity operator and $T$ is a compact linear operator) with a deviation less then $| α |$ ; on the other hand, such approximability turns out to be...

A theorem on continuous dependence on a parameter

Karel Karták (1966)

Časopis pro pěstování matematiky

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Angular limits of the integrals of the Cauchy type

Josef Král, Dagmar Medková (1997)

Czechoslovak Mathematical Journal

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Integrals of the Cauchy type extended over the boundary $\partial A$ of a general compact set $A$ in the complex plane are investigated. Necessary and sufficient conditions on $\partial A$ are established guaranteeing the existence of angular limits of these integrals at a fixed $z \in \partial A$ for all densities satisfying a Hölder-type condition at $z$ .