Results 1 to 10 of about 4,934,927 (307)
Dirac--Sobolev Spaces and Sobolev Spaces [PDF]
arXiv, 2010 The aim of this work is to study the first order Dirac-Sobolev spaces in $L^p$ norm on an open subset of ${\mathbb R}^3$ to clarify its relationship with the corresponding Sobolev spaces. It is shown that for $1< p <\infty$, they coincide, while for $p=1$, the latter spaces are proper subspaces of the former.
Yoshimi Saito, Takashi Ichinose
arxiv +5 more sources
Lifting in Sobolev spaces [PDF]
Journal d'Analyse Mathématique, 2000 We characterize the couples $(s,p)$ with the following property: if $u$ is a complex-valued unimodular map in $W^{s,p}$, then $u$ has (locally) a phase in $W^{s,p}$.
Jean Bourgain +2 more
openalex +6 more sources
Topology and Sobolev Spaces [PDF]
Journal of Functional Analysis, 2001 AbstractConsider the Sobolev class W1, p(M, N) where M and N are compact manifolds. We present some sufficient conditions which guarantee that W1, p(M, N) is path-connected. We also discuss cases where W1, p(M, N) admits more than one component. There are still a number of open problems, especially concerning the values of p where a change in homotopy ...
Haïm Brézis, Yanyan Li
openalex +4 more sources
Equivalent Norms for Sobolev Spaces [PDF]
Proceedings of the American Mathematical Society, 1970 where ...
Robert Adams
openalex +3 more sources
Inequalities in the most simple Sobolev space and convolutions of 𝐿₂ functions with weights [PDF]
, 1993 For the most simple Sobolev space on R composed of real-valued and absolutely continuous functions f(x) on R with finite norms too 2f() 2( 1/2 (a 2 b dx (a, b > 0), -00 we shall apply the theory of reproducing kernels, and derive natural norm ...
Saburou Saitoh
openalex +2 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
On a new fractional Sobolev space with variable exponent on complete manifolds
Boundary Value Problems, 2022 We present the theory of a new fractional Sobolev space in complete manifolds with variable exponent. As a result, we investigate some of our new space’s qualitative properties, such as completeness, reflexivity, separability, and density.
A. Aberqi +3 more
semanticscholar +1 more source
On fractional Orlicz–Sobolev spaces [PDF]
Analysis and Mathematical Physics, 2021 AbstractSome recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings.
Angela Alberico +3 more
openaire +4 more sources
Transition Threshold for the 3D Couette Flow in Sobolev Space [PDF]
Communications on Pure and Applied Mathematics, 2018 In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number Re. It was proved that if the initial velocity v0 satisfies ∥v0−y,0,0∥H2≤c0Re−1 for some c0 > 0 independent of Re, then the solution of the ...
Dongyi Wei, Zhifei Zhang
semanticscholar +1 more source
Basic results of fractional Orlicz-Sobolev space and applications to non-local problems [PDF]
Topological Methods in Nonlinear Analysis, 2019 In this paper, we study the interplay between Orlicz-Sobolev spaces $L^{M}$ and $W^{1,M}$ and fractional Sobolev spaces $W^{s,p}$. More precisely, we give some qualitative properties of the new fractional Orlicz-Sobolev space $W^{s,M}$, where $s\in (0,1)$
S. Bahrouni, H. Ounaies, L. S. Tavares
semanticscholar +1 more source