Results 1 to 10 of about 467 (161)
Weighted Variable Sobolev Spaces and Capacity [PDF]
Journal of Function Spaces and Applications, 2012 We define weighted variable Sobolev capacity and discuss properties of capacity in the space 𝑊1,𝑝(⋅)(ℝ𝑛,𝑤). We investigate the role of capacity in the pointwise definition of functions in this space if the Hardy-Littlewood maximal operator is bounded on ...
Ismail Aydin
doaj +2 more sources
A new approach to weighted Sobolev spaces. [PDF]
Mon Hefte MathAbstract We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least one of the weight functions is very small.
Kebiche D.
europepmc +7 more sources
On the trace space of a Sobolev space with a radial weight [PDF]
Journal of Function Spaces and Applications, 2008 Our concern in this paper lies with trace spaces for weighted Sobolev spaces, when the weight is a power of the distance to a point at the boundary. For a large range of powers we give a full description of the trace space.
Helmut Abels +2 more
doaj +3 more sources
Interpolation of weighted Sobolev spaces [PDF]
Journal of Functional Analysis, 2019 In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can obtain an analogue of the famous Stein-Weiss theorem for weighted $L^{p}$ spaces. We consider an example which gives some indication that this may not be possible in all cases.
Amit Einav
exaly +4 more sources
Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 We study in this paper a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of ℝ𝑛, 𝑛≥3. We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem.
Serena Boccia +2 more
doaj +5 more sources
The Zakharov–Kuznetsov equation in weighted Sobolev spaces
Journal of Mathematical Analysis and Applications, 2016 In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov-Kuznetsov equation $$\left. \begin{array}{rl} u_t+\partial_x^3 u+\partial_x \partial_y^2 u +u \partial_x u &\hspace{-2mm}=0,\qquad\qquad (x,y)\in\mathbb R^2,\; t\in\mathbb R,\\ u(x,y,0)&\hspace{-2mm}=u_0(x,y).
JOSÉ Jiménez Urrea +2 more
exaly +3 more sources
Multipliers in weighted Sobolev spaces on the axis [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 This work establishes necessary and sufficient conditions for the boundedness of one variable differential operator acting from a weighted Sobolev space Wlp,v to a weighted Lebesgue space on the positive real half line.
A. Myrzagaliyeva
doaj +2 more sources
Anisotropic Sobolev Spaces with Weights
Tokyo Journal of Mathematics, 2023 We study Sobolev spaces with weights in the half-space $\mathbb{R}^{N+1}_+=\{(x,y): x \in \mathbb{R}^N, y>0\}$, adapted to the singular elliptic operators \begin{equation*} \mathcal L =y^{α_1}Δ_{x} +y^{α_2}\left(D_{yy}+\frac{c}{y}D_y -\frac{b}{y^2}\right). \end{equation*}
Metafune G., Negro L., Spina C.
openaire +3 more sources
Geometric ergodicity in a weighted Sobolev space [PDF]
The Annals of Probability, 2020 For a discrete-time Markov chain $\{X(t)\}$ evolving on $\Re^\ell$ with transition kernel $P$, natural, general conditions are developed under which the following are established: 1. The transition kernel $P$ has a purely discrete spectrum, when viewed as a linear operator on a weighted Sobolev space $L_\infty^{v,1}$ of functions with norm, $$ \|f\|_{v,
Devraj, Adithya +2 more
openaire +4 more sources
Lupaş-type inequality and applications to Markov-type inequalities in weighted Sobolev spaces
Bulletin of Mathematical Sciences, 2021 Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. In particular, analytic properties of such polynomials have been extensively studied, mainly focused on their asymptotic behavior and the location of their zeros. On
Francisco Marcellán +1 more
doaj +1 more source