Results 281 to 290 of about 5,040,927 (317)
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Tractability of Multivariate Approximation over a Weighted Unanchored Sobolev Space
, 2009We study d-variate L2-approximation for a weighted unanchored Sobolev space having smoothness m≥1. This space is equipped with an unusual norm which is, however, equivalent to the norm of the d-fold tensor product of the standard Sobolev space. One might
A. Werschulz, H. Wozniakowski
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Zero Distribution and Behavior of Orthogonal Polynomials in the Sobolev Space $W^{1,2} [ - 1,1]$
, 1975The distribution of the zeros of the polynomials orthogonal in the Sobolev space $W^{1,2} [ - 1,1]$ with constant weights is established within a certain range of values of the parameters by relating the zeros to the zeros of the Legendre polynomials. In
E. A. Cohen
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Hardy's Inequality in a Variable Exponent Sobolev Space
Georgian Mathematical Journal, 2005We show that a norm version of Hardy's inequality holds in a variable exponent Sobolev space provided the maximal operator is bounded. Our proof uses recent local versions of the inequality for a fixed exponent.
Petteri Harjulehto, P. Hst, M. Koskenoja
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Spectral Approximation Orders of Radial Basis Function Interpolation on the Sobolev Space
SIAM Journal on Mathematical Analysis, 2001In this study, we are mainly interested in error estimates of interpolation, using smooth radial basis functions such as multiquadrics. The current theories of radial basis function interpolation provide optimal error bounds when the basis function $\phi$
Jungho Yoon
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, 2005
We present a direct proof of the discrete Poincaré–Friedrichs inequalities for a class of nonconforming approximations of the Sobolev space H 1(Ω), indicate optimal values of the constants in these inequalities, and extend the discrete Friedrichs ...
M. Vohralík
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We present a direct proof of the discrete Poincaré–Friedrichs inequalities for a class of nonconforming approximations of the Sobolev space H 1(Ω), indicate optimal values of the constants in these inequalities, and extend the discrete Friedrichs ...
M. Vohralík
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An exterior boundary-value problem for the Maxwell equations with boundary data in a Sobolev space
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1988Synopsis We treat the time-harmonic Maxwell equations in an exterior domain with prescribed boundary data [n, E] in the Sobolev space of square integrable tangential fields with square integrable surface divergence.
P. Hähner
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Canadian Journal of Mathematics, 1996
AbstractWe study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains𝓓when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the MuckenhouptApclass locally in 𝓓. Moreover, when the weightswi(x) are of the form dist(x,Mi)αi,αi∈ ℝ,Mi⊂ 𝓓that are doubling, we are
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AbstractWe study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains𝓓when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the MuckenhouptApclass locally in 𝓓. Moreover, when the weightswi(x) are of the form dist(x,Mi)αi,αi∈ ℝ,Mi⊂ 𝓓that are doubling, we are
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Distributions and Sobolev Spaces [PDF]
, 2015 We have seen the concept of Dirac measure arising in connection with the fundamental solutions of the diffusion and the wave equations. Another interesting situation is the following, where the Dirac measure models a mechanical impulse.
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Sobolev space preconditioning for Newton's method using domain decomposition
Numerical Linear Algebra with Applications, 2002An inner–outer iteration is constructed for ill‐conditioned non‐linear elliptic boundary value problems, using a damped inexact Newton Method for the outer and a conjugate gradient method for the inner iteration. The focus is on efficient preconditioning
O. Axelsson, I. Faragó, J. Karátson
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Sobolev inequalities on homogeneous spaces
Potential Analysis, 1995We consider a homogeneous space X = (X, d, m) of dimension ν ≥ 1 and a local regular Dirichlet form a in L 2(X, m). We prove that if a Poincare inequality of exponent 1 ≤ p < ν holds on every pseudo-ball B(x, R) of X, then Sobolev and Nash inequalities of any exponent q ∈ [p, ν), as well as Poincare inequalities of any exponent q ∈ [p, +∞), also hold ...
BIROLI, MARCO, MOSCO U.
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