Results 41 to 50 of about 1,651 (223)
, 2022 We investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), (r = 1, 2,...), by the Hardy averaging operator A (f) (x) = 1/x integral(x)(0) f (t)dt. If the function f lies in
Ayazoglu, Rabil +3 more
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Parabolic weighted Sobolev-Poincaré type inequalities
, 2022 Diening L, Lee M, Ok J. Parabolic weighted Sobolev-Poincaré type inequalities. Nonlinear Analysis : Theory, Methods & Applications . 2022;218: 112772.We derive weighted Sobolev-Poincare type inequalities in function spaces concerned with parabolic ...
Diening, Lars ; https://orcid.org/ +2 more
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Elastic scattering by unbounded rough surfaces: Solvability in weighted Sobolev spaces [PDF]
, 2013 This paper is concerned with the variational approach in weighted Sobolev spaces to time-harmonic elastic scattering by two-dimensional unbounded rough surfaces.
Elschner, Johannes, Hu, Guanghui
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Final State Problem for the Dirac-Klein-Gordon Equations in Two Space Dimensions
Abstract and Applied Analysis, 2013 We study the final state problem for the Dirac-Klein-Gordon equations (DKG) in two space dimensions. We prove that if the nonresonance mass condition is satisfied, then the wave operator for DKG is well defined from a neighborhood at the origin in lower ...
Masahiro Ikeda
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Weighted fractional Sobolev spaces as interpolation spaces in bounded domains
, 2022 We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the ...
Acosta Rodriguez, Gabriel +7 more
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Sobolev–Hardy space with general weight
Journal of Mathematical Analysis and Applications, 2006 In this paper, the authors prove the following \(k\)th order Hardy inequality with general weight. Let \(\Omega\) be a bounded domain. Then, under the assumptions \((H_1)\) and \((H_2)\), for each positive integer \(k\) the inequality \[ \int_{\Omega}\phi|\nabla u|^2\,dx-\int_{\Omega}\phi\sum_{i=1}^{k}\left(\frac{h_i'}{h_i}\right)^2u^2\,dx\geq\int_ ...
Shen, Yaotian, Chen, Zhihui
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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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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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Open Mathematics, 2016 We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients.
Guliyev Vagif S., Omarova Mehriban N.
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