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

Josef Král, Wolfgang L. Wendland (1986)

Aplikace matematiky

Simple examples of bounded domains D 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 possible for...

Some remarks on the existence of a resolvent

Masanori Kishi (1975)

Annales de l'institut Fourier

Noting that a resolvent is associated with a convolution kernel x satisfying the domination principle if and only if x has the dominated convergence property, we give some remarks on the existence of a resolvent.

Symmetry problems 2

N. S. Hoang, A. G. Ramm (2009)

Annales Polonici Mathematici

Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.

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