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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 $D \subset 𝐑^{3}$ 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 possible for...

Some properties of functions with bounded mean oscillation

Umberto Neri (1977)

Studia Mathematica

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.

Stability of Lewis and Vogel's result.

D. Preiss, T. Toro (2007)

Revista Matemática Iberoamericana

Sul problema di Dirichlet in un cono per l’equazione $Δ^{m} u = f$

Antonio Bove (1975)

Rendiconti del Seminario Matematico della Università di Padova

Superharmonic functions on Lipschitz domain

Martin Silverstein, Richard Wheeden (1971)

Studia Mathematica

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.