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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 orthogonal decompositions of Sobolev spaces and applications

H. Begehr, Yu. Dubinskiĭ (2001)

Colloquium Mathematicae

Two kinds of orthogonal decompositions of the Sobolev space W̊₂¹ and hence also of W ₂ - 1 for bounded domains are given. They originate from a decomposition of W̊₂¹ into the orthogonal sum of the subspace of the Δ k -solenoidal functions, k ≥ 1, and its explicitly given orthogonal complement. This decomposition is developed in the real as well as in the complex case. For the solenoidal subspace (k = 0) the decomposition appears in a little different form. In the second kind decomposition the Δ k -solenoidal...

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.

Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains

Tadie (1999)

Applications of Mathematics

In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder ( r ≤ d ) where ( r , θ , z ) denotes the cylindrical co-ordinates in ℝ 3 is considered. The motion is with swirl (i.e. the θ -component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. that for the problem without swirl ( f q = 0 in (f)) in the whole space, as the flux constant k tends to ∞ , 1) dist ( 0 z , ∂ A ) = O ( k 1 / 2 ) ; diam A = O ( exp ( - c 0 k 3 / 2 ) ) ; 2) ( k 1 / 2 Ψ ) k ∈ ℕ converges to a vortex cylinder U m (see...

Su alcune questioni connesse con il problema di derivata obliqua regolare per le funzioni armoniche

Enrico Magenes (1990)

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

— Vengono riconsiderati il problema di derivata obliqua regolare e quello misto di Dirichlet-derivata obliqua regolare per le funzioni armoniche in un dominio di R 3 e le questioni di completezza hilbertiana connesse già studiate in un precedente lavoro e viene data una nuova dimostrazione di un teorema di unicità.

Superharmonic extension and harmonic approximation

Stephen J. Gardiner (1994)

Annales de l'institut Fourier

Let Ω be an open set in ℝ n and E be a subset of Ω . We characterize those pairs ( Ω , E ) which permit the extension of superharmonic functions from E to Ω , or the approximation of functions on E by harmonic functions on Ω .

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