Results 1 to 10 of about 4,761,041 (315)
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 $W^{s,p}$.
Bourgain, Jean +2 more
openaire +6 more sources
Topology and Sobolev Spaces [PDF]
Journal of Functional Analysis, 2000 Let two compact connected oriented smooth Riemannian manifolds \(M\) and \(N\) (with or without boundary) be given. It is supposed that \(\dim M\geq 2\); the example \(N=S^1\) is of importance. Let \(W^{1,p}(M,N)\) be the Sobolev space of functions \(u\in W^{1,p} (M,\mathbb{R}^k)\) with \(u(x)\in N\) a.e.
Haim Brezis, Yanyan Li
openaire +5 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
A First Course in Fractional Sobolev Spaces [PDF]
Graduate Studies in Mathematics, 2023 This book provides a gentle introduction to fractional Sobolev spaces, which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It
G. Leoni
semanticscholar +1 more source
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
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
Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2019 In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional Orlicz-Sobolev ...
S. Bahrouni, H. Ounaies
semanticscholar +1 more source
Журнал Белорусского государственного университета: Математика, информатика, 2020 Let (X, d, µ) be a doubling metric measure space with doubling dimension γ, i. e. for any balls B(x, R) and B(x, r), r < R, following inequality holds µ(B(x, R)) ≤ aµ (R/r)γµ(B(x, r)) for some positive constants γ and aµ.
Sergey A. Bondarev
doaj +1 more source
On anisotropic Sobolev spaces [PDF]
Communications in Contemporary Mathematics, 2019 We investigate two types of characterizations for anisotropic Sobolev and BV spaces. In particular, we establish anisotropic versions of the Bourgain–Brezis–Mironescu formula, including the magnetic case both for Sobolev and BV functions.
Hoai-Minh Nguyen, Marco Squassina
openaire +5 more sources