Results 11 to 20 of about 5,040,878 (277)
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
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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
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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
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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
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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
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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
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Topology and Sobolev Spaces [PDF]
Journal of Functional Analysis, 2000 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 ...
Haim Brezis, Yanyan Li
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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
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AIMS Mathematics, 2022 This paper considers a simplified three dimensional Ericksen-Leslie System for nematic liquid crystal flows in the unbounded domain $ \Omega: = \mathbb R^+\times \mathbb R^2 $ or the smooth bounded domain $ \Omega $.
Junling Sun, Xuefeng Han
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The necessary and sufficient conditions for wavelet frames in Sobolev space over local fields
Boletim da Sociedade Paranaense de Matemática, 2020 In this paper we construct wavelet frame on Sobolev space. A necessary condition and suffcient conditions for wavelet frames in Sobolev space are given.
Ashish Pathak +2 more
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