Rate of convergence in singular perturbations

Wilfred M. Greenlee

Displaying similar documents to “Rate of convergence in singular perturbations”

Theory of Bessel potentials. III : potentials on regular manifolds

Robert Adams, Nachman Aronszajn, M. S. Hanna (1969)

Annales de l'institut Fourier

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In this paper Bessel potentials on $C^{\infty}$ -Riemannian manifolds (open or bordered) are studied. Let $M$ be an $n$ -dimensional manifold, and $N$ a submanifold of $M$ of dimension $k$ . Sufficient conditions are given for: 1) the restriction to $N$ of any potential of order $α$ on $M$ to be a potential of order $α - \frac{n - k}{2}$ on $N$ ; 2) any potential of order $α - \frac{n - k}{2}$ on $N$ to be extendable to a potential of order $α$ on $M$ . It is also proved that for a bordered manifold $M$ the restriction to its interior $M^{i}$ is an isometric isomorphism...

Theory of Bessel potentials. II

Robert Adams, Nachman Aronszajn, K. T. Smith (1967)

Annales de l'institut Fourier

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Dans cette partie de la théorie des potentiels besseliens on considère les restrictions de potentiels de la classe $P^{a} (R^{n})$ aux domaines ouverts $D \subset R^{n}$ . On cherche à caractériser de manière intrinsèque la classe $P^{a} (D)$ ainsi obtenue. On attaque ce problème en définissant de manière directe (§ 2) une classe ${\overset{ˇ}{P}}^{a} (D) \subset P^{a} (D)$ qui, pour des domaines assez réguliers, est égale à $P^{a} (D)$ . L’égalité $P^{a} (D) = P^{a} (D)$ est équivalente à l’existence d’un opérateur-extension $E : {\overset{ˇ}{P}}^{a} (D) \to P^{a} (R^{n})$ , linéaire et continu, tel que $E u$ soit une extension...

A multilinear interpolation theorem

Misha Zafran (1978)

Studia Mathematica

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Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown, Don B. Hinton (1999)

Mathematica Bohemica

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We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in $ℝ^{n}$ . Also, for symmetric second-order ordinary differential operators we show that ${lim sup}_{t \to c} {(p q^{'})}^{'} / q^{2} = θ < 2$ where $c$ is a singular point guarantees separation of $- {(p y^{'})}^{'} + q y$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $- Δ y + q y$ is separated on its minimal domain if $q$ is superharmonic. For $n = 1$ the...

Boundary values for Sobolev-spaces with weights. Density of $D (Ω) in W_{p, γ_{0}, \dots, γ_{r}}^{s} (Ω) and in H_{p, γ_{0}, \dots, γ_{r}}^{s} (Ω)$ for $s$ > $0$ and $r = {[s - \frac{1}{p}]}^{-}$

Hans Triebel (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On duality and interpolation for spaces of polyharmonic functions

Ewa Ligocka (1988)

Studia Mathematica

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Displaying similar documents to “Rate of convergence in singular perturbations”

Theory of Bessel potentials. III : potentials on regular manifolds

Theory of Bessel potentials. II

A multilinear interpolation theorem

Two separation criteria for second order ordinary or partial differential operators

Boundary values for Sobolev-spaces with weights. Density of D ( Ω ) in W p , γ 0 , ⋯ , γ r s ( Ω ) and in H p , γ 0 , ⋯ , γ r s ( Ω ) for s &gt; 0 and r = s - 1 p -

On duality and interpolation for spaces of polyharmonic functions

Boundary values for Sobolev-spaces with weights. Density of $D (Ω) in W_{p, γ_{0}, \dots, γ_{r}}^{s} (Ω) and in H_{p, γ_{0}, \dots, γ_{r}}^{s} (Ω)$ for $s$ > $0$ and $r = {[s - \frac{1}{p}]}^{-}$