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Density Results in sobolev spaces Whose Elements Vanish on a Part of the Boundary

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Chinese Annals of Mathematics,Series B 2011年第6期32卷 823-846页

作者： Jean-Marie Emmanuel BERNARD Laboratoire Analyse et Probabitilités Université d'Evry val d'Essonne23 Boulevard de France91037 EVRYFrance

This paper is devoted to the study of the subspace of Wm＇＂ of functions that vanish on a part γ0 of the boundary. The author gives a crucial estimate of the Poincare constant in balls centered on the boundary of γ0. Then, the convolution-translation method, a variant of the standard mollifier technique, can be used to prove the density of smooth functions that vanish in a neighborhood of γ0, in this subspace. The result is first proved for m = 1, then generalized to the case where m 〉 1, in any dimension, in the framework of Lipschitz-continuous domain. However, as may be expected, it is needed to make additional assumptions on the boundary of γ0, namely that it is locally the graph of some Lipschitz-continuous function.

关键词： Density results Boundary value problems sobolev spaces

A CHARACTERIZATION OF ORTHONORMAL WAVELET FAMILIES IN sobolev spaces

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Acta Mathematica Scientia 2011年第4期31卷 1475-1488页

作者：鲁大勇李登峰 Institute of Applied Mathematics College of Mathematics and Information Science Henan University College of Mathematics and Statistics Wuhan University

In this paper, a characterization of orthonormal wavelet families in sobolev spaces H s （R） is established.

关键词： wavelets orthonormal wavelet families sobolev spaces

Weinstein–sobolev spaces of Exponential Type and Applications

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Acta Mathematica Sinica,English Series 2013年第3期29卷 591-608页

作者： Hassen BEN MOHAMED Belgacem GHRIBI Department of Mathematics Faculty of Sciences of Gabs

In this paper, we introduce and study the sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, including completeness and imbedding theorem, are proved. Finally, using the theory of reproducing kernels, some applications are given for these spaces.

关键词： Weinstein operator Weinstein transform distribution sobolev spaces

LOCAL WELL-POSEDNESS IN sobolev spaces WITH NEGATIVE INDICES FOR A SEVENTH ORDER DISPERSIVE EQUATION

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Acta Mathematica Scientia 2014年第1期34卷 199-208页

作者：王宏伟 Department of Mathematics Anyang Normal University

This paper is concerned with the Cauchy problem of a seventh order dispersive equation. We prove local well-posedness with initial data in sobolev spaces Hs（R） for negative indices of s〉-114 .

关键词： Cauchy problem local well-posedness sobolev spaces bilinear estimate

PRECISE SMOOTHING EFFECTS OF HOMOGENEOUS LANDAU EQUATION IN sobolev spaces

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Acta Mathematica Scientia 2012年第3期32卷 1245-1254页

作者： Mohamed Najeme Universit'e de Rouen UMR-6085Math'ematiques76801 Saint Etienne du RouvrayFrance

In this work, we study the smoothing effect of Cauchy problem in sobolev space for the spatially homogeneous Landau equation in the Maxwellian case. We obtain a precise estimate with respect to time variable, which im... 详细信息

关键词： Landau equation smoothing effect of Cauchy problem sobolev spaces

Multi-Wavelet Bessel Sequences in sobolev spaces

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Journal of Mathematical Research with Applications 2018年第5期38卷 487-495页

作者： Jianping ZHANG Chuanli CAI College of Mathematics and Computer Science Yan'an University

Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these spaces.

关键词： multi-wavelet Bessel sequence frame sobolev spaces

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN sobolev spaces W^(m,p)(Ω)

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Applied Mathematics and Mechanics(English Edition) 1992年第3期13卷 273-279页

作者： Ling Yong-yong Department of Applied Mathematics Tongji UniversityShanghai

In the present paper the concept and properties of the residual functional in sobolev space are *** weak compactness,force condition,lower semi-continuity and convex of the residual functional are *** sobolev space,the minimum principle of the residual functional is *** minimum existence theoreomfor J(u)=0 is given by the modern critical point *** the equivalence theorem or five equivalence forms for the residual functional equation are also proved.

关键词： sobolev spaces residual functional infinite Banach spaces convex lower semi-continuity force condition minimum existence theorem

New sobolev-Weinstein spaces and Applications

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Journal of Mathematical Research with Applications 2022年第3期42卷 247-260页

作者： Hassen BEN MOHAMED Youssef BETTAIBI Department of Mathematics Faculty of Sciences Gabes University

In this paper, we consider the generalized Weinstein operator■ we introduce new sobolev-Weinstein spaces denoted ■associated with the generalized Weinstein operator and we investigate their properties. Next, as appl... 详细信息

关键词： generalized Weinstein operator generalized Weinstein transform sobolev spaces extremal functions reproducing kernels

sobolev Mapping of the Bergman Projections on Generalized Hartogs Triangles

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Acta Mathematica Sinica,English Series 2024年第2期40卷 451-466页

作者： Hong Yan LIU Zhen Han TU School of Mathematics and Statistics Wuhan UniversityWuhan 430072P.R.China

In this paper,we investigate sobolev mapping properties of the Bergman *** domain we focus on is defined byΩm/n:={(z,w)∈C^(1+N):|w1|<|z|m1/n1<1,…|wN|<|z|/m_(N)/n_(N)<1},where m=(m1,…mN)∈(Z^(+))^(N),n=(n1,…nN)∈(... 详细信息

In this paper,we investigate sobolev mapping properties of the Bergman *** domain we focus on is defined byΩm/n:={(z,w)∈C^(1+N):|w1|sobolev irregularity of the Bergman projections on 2 is *** also prove some sobolev regularity results of the Bergman projections onΩm/n for m=(1,…1).

关键词： Bergman projections generalized Hartogs triangles sobolev spaces