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Analysis of direct segregated boundary-domain integral equations for variable-coefficient mixed bvps in exterior domains [PDF]
, 2013 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 World Scientific Publishing.Direct segregated systems of boundary-domain integral equations are formulated for the mixed (
Mikhailov, SE +2 more
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Weighted Norm Estimates for Sobolev Spaces [PDF]
Transactions of the American Mathematical Society, 1987 We give sufficient conditions for estimates of the form\[∫|u(x)|qdμ(x)⩽C‖u‖s,p1,u∈Hs,p,{\int {\left | {u(x)} \right |} ^q}d\mu (x) \leqslant C\left \| u \right \|_{s,p}^1,\qquad u \in {H^{s,p}},\]to hold, whereμ(x)\mu (x)is a measure and‖u‖s,p{\left \| u \right \|_{s,p}}is the norm of the Sobolev spaceHs,p{H^{s,p}}.
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Trace theorems for Sobolev-Slobodeckij spaces with or without weights
Journal of Function Spaces and Applications, 2007 We prove that the well-known trace theorem for weighted Sobolev spaces holds true under minimal regularity assumptions on the domain. Using this result, we prove the existence of a bounded linear right inverse of the trace operator for Sobolev ...
Doyoon Kim
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Nonlinear Analysis, 2022 In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = Wω1,1 (a,b) x Wω1,1 (a,b).
Taqi A.M. Shatnawi +3 more
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Real Interpolation of Sobolev Spaces Associated to a Weight [PDF]
Potential Analysis, 2009 25 ...
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Weierstrass' Theorem in Weighted Sobolev Spaces
Journal of Approximation Theory, 2001 It is very well known that given any compact interval \(I\), the set of all continuous (almost everywhere) functions \(C(I)\) on \(I\) is the biggest set of functions that can be approximated by polynomials in the \(L^\infty(I)\) norm. This result is the very classical Weierstrass' Theorem. There are many generalizations of this result [see e.g.
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Component-by-component construction of good intermediate-rank lattice rules
, 2003 It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces.
Joe, Stephen, Kuo, Frances Y.
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Sampling in a weighted Sobolev space
Comptes Rendus. Mathématique, 2012 We show that functions f in some weighted Sobolev space are completely determined by time-frequency samples { f (
Acala, Nestor G., Reyes, Noli N.
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Advanced Materials, EarlyView.Residual magnetization induces pronounced mechanical anisotropy in ultra‐soft magnetorheological elastomers, shaping deformation and actuation even without external magnetic fields. This study introduces a computational‐experimental framework integrating magneto‐mechanical coupling into topology optimization for designing soft magnetic actuators with ...
Carlos Perez‐Garcia +3 more
wiley +1 more source
Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy
, 2006 The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point rank-1 lattice rules whose weighted
Joe, Stephen
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