Results 61 to 70 of about 5,040,927 (317)
Journal of Mathematical Analysis and Applications, 2011 AbstractFix strictly increasing right continuous functions with left limits and periodic increments, Wi:R→R, i=1,…,d, and let W(x)=∑i=1dWi(xi) for x∈Rd. We construct the W-Sobolev spaces, which consist of functions f having weak generalized gradients ∇Wf=(∂W1f,…,∂Wdf).
Alexandre B. Simas, Fábio J. Valentim
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A note on the Malliavin–Sobolev spaces [PDF]
Statistics & Probability Letters, 2016 In this paper, we provide a strong formulation of the stochastic G{ }teaux differentiability in order to study the sharpness of a new characterization, introduced in [6], of the Malliavin-Sobolev spaces. We also give a new internal structure of these spaces in the sense of sets inclusion.
Imkeller, Peter +3 more
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Multivariate box spline wavelets in higher-dimensional Sobolev spaces
Journal of Inequalities and Applications, 2018 We construct wavelets and derive a density condition of MRA in a higher-dimensional Sobolev space. We give necessary and sufficient conditions for orthonormality of wavelets in Hs(Rd) $H^{s}(\mathbb {R}^{d})$.
Raj Kumar, Manish Chauhan
doaj +1 more source
Composition operators on Sobolev spaces, $Q$-mappings and weighted Sobolev inequalities [PDF]
arXiv, 2021 In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and $Q$-mappings. On this base we obtain measure distortion properties $Q$-homeomorphisms. Using the composition operators on Sobolev spaces we obtain weighted Sobolev inequalities with special weights which are Jacobians of $Q$-mappings.
arxiv
, 2019 We prove an optimal order error bound in the discrete $H^2(\Omega)$ norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in $n$ space dimensions, with $n \in \{2,\dots,7\}$, whose generalized solution ...
Müller, Stefan +2 more
core +1 more source
What is a Sobolev space for the Laguerre function systems
, 2008 We discuss the concept of Sobolev space associated to the Laguerre operator $ L_\al = - y\,\frac{d^2}{dy^2} - \frac{d}{dy} + \frac{y}{4} + \frac{\al^2}{4y},\quad y\in (0,\infty).$ We show that the natural definition does not fit with the concept of ...
B. Bongioanni, J. Torrea
semanticscholar +1 more source
On the constants for multiplication in Sobolev spaces
Advances in Applied Mathematics, 2006 For n > d/2, the Sobolev (Bessel potential) space H^n(R^d, C) is known to be a Banach algebra with its standard norm || ||_n and the pointwise product; so, there is a best constant K_{n d} such that || f g ||_{n} <= K_{n d} || f ||_{n} || g ||_{n} for all f, g in this space.
C. Morosi, L. Pizzocchero
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Optimal stencils in Sobolev spaces [PDF]
IMA Journal of Numerical Analysis, 2017 This paper proves that the approximation of pointwise derivatives of order $s$ of functions in Sobolev space $W_2^m(\R^d)$ by linear combinations of function values cannot have a convergence rate better than $m-s-d/2$, no matter how many nodes are used for approximation and where they are placed.
Davydov, Oleg, Schaback, Robert
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G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE [PDF]
, 2014 We introduce a new notion of G-expectation-weighted Sobolev spaces, or in short, G-Sobolev spaces, and prove that a backward SDEs driven by G-Brownian motion are in fact path dependent PDEs in the corresponding Sobolev spaces under G-norms.
Peng, Shige, Song, Yongsheng
core
First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, EarlyView.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley +1 more source