Results 51 to 60 of about 4,722,250 (284)

Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets

, 2015
We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with ...
Björn, Anders, Björn, Jana, Latvala, Visa   +2 more
core   +1 more source

W-Sobolev spaces

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
openaire   +2 more sources

Uhlenbeck’s Decomposition in Sobolev and Morrey–Sobolev Spaces [PDF]

Results in Mathematics, 2018
We present a self-contained proof of Uhlenbeck's decomposition theorem for $ \in L^p(\mathbb{B}^n,so(m)\otimes ^1\mathbb{R}^n)$ for $p\in (1,n)$ with Sobolev type estimates in the case $p \in[n/2,n)$ and Morrey-Sobolev type estimates in the case $p\in (1,n/2)$.
Anna Zatorska-Goldstein, Paweł Goldstein   +1 more
openaire   +3 more sources

Weighted Variable Sobolev Spaces and Capacity

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   +1 more source

A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces

Journal of Inequalities and Applications, 2016
In recent years, nonhomogeneous wavelet frames have attracted some mathematicians’ interest. This paper investigates such problems in a Sobolev space setting. A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces pairs is obtained.
Jian-Ping Zhang, Yun-Zhang Li
doaj   +1 more source

Some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $

AIMS Mathematics, 2022
In this paper, some sharp Sobolev inequalities on $ BV({\mathbb{R}}^n) $, the space of functions of bounded variation on $ {\mathbb{R}}^n $, $ n\geq 2 $, are deduced through the $ L_p $ Brunn-Minkowski theory.
Jin Dai , Shuang Mou
doaj   +1 more source

Sobolev spaces on warped products [PDF]

Journal of Functional Analysis, 2018
Corrected few typos in the previous version and updated the ...
Gigli, Nicola, Han, Bang-Xian
openaire   +4 more sources

Variable Exponent Spaces of Differential Forms on Riemannian Manifold

Journal of Function Spaces and Applications, 2012
We introduce the Lebesgue space and the exterior Sobolev space for differential forms on Riemannian manifold 𝑀 which are the Lebesgue space and the Sobolev space of functions on 𝑀, respectively, when the degree of differential forms to be zero.
Yongqiang Fu, Lifeng Guo
doaj   +1 more source

Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
wiley   +1 more source

Clarkson’s Inequalities for Periodic Sobolev Space [PDF]

Учёные записки Казанского университета: Серия Физико-математические науки, 2016
The paper is devoted to developing the proof of Clarkson's inequalities for periodic functions belonging to the Sobolev space. The norm of the space has not been considered earlier.
I.V. Korytov
doaj