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《Journal de Mathématiques Pures et Appliquées》2006,85(1):2-16
Let ω be a domain in and let be a smooth immersion. The main purpose of this paper is to establish a “nonlinear Korn inequality on the surface ”, asserting that, under ad hoc assumptions, the -distance between the surface and a deformed surface is “controlled” by the -distance between their fundamental forms. Naturally, the -distance between the two surfaces is only measured up to proper isometries of .This inequality implies in particular the following interesting per se sequential continuity property for a sequence of surfaces. Let , , be mappings with the following properties: They belong to the space ; the vector fields normal to the surfaces , , are well defined a.e. in ω and they also belong to the space ; the principal radii of curvature of the surfaces , , stay uniformly away from zero; and finally, the fundamental forms of the surfaces converge in toward the fundamental forms of the surface as . Then, up to proper isometries of , the surfaces converge in toward the surface as .Such results have potential applications to nonlinear shell theory, the surface being then the middle surface of the reference configuration of a nonlinearly elastic shell. 相似文献
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Philippe G. Ciarlet Liliana Gratie Cristinel Mardare 《Comptes Rendus Mathematique》2005,341(3):201-206
The main purpose of this Note is to show how a ‘nonlinear Korn's inequality on a surface’ can be established. This inequality implies in particular the following interesting per se sequential continuity property for a sequence of surfaces. Let ω be a domain in , let be a smooth immersion, and let , , be mappings with the following properties: They belong to the space ; the vector fields normal to the surfaces , , are well defined a.e. in ω and they also belong to the space ; the principal radii of curvature of the surfaces stay uniformly away from zero; and finally, the three fundamental forms of the surfaces converge in toward the three fundamental forms of the surface as . Then, up to proper isometries of , the surfaces converge in toward the surface as . To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). 相似文献
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胡国恩 《数学物理学报(B辑英文版)》2005,25(3):545-554
Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the Lp(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn))boundedness for the corresponding commutators. A new interpolation theorem is also established. 相似文献
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Douglas P. Hardin Michael C. Northington Alexander M. Powell 《Applied and Computational Harmonic Analysis》2018,44(2):294-311
A sharp version of the Balian–Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators must satisfy , namely, . Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space ; our results provide an absolutely sharp improvement with . Our results are sharp in the sense that cannot be replaced by for any . 相似文献
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《Journal of Mathematical Analysis and Applications》2014,419(2):783-795
We study restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension d is even, then it is conjectured that the Stein–Tomas restriction result can be improved to the estimate for both spheres and paraboloids in finite fields. In this paper we show that the conjectured restriction estimate holds in the specific case when test functions under consideration are restricted to d-coordinate functions or homogeneous functions of degree zero. To deduce our result, we use the connection between the restriction phenomena for our varieties in d dimensions and those for homogeneous varieties in dimensions. 相似文献
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Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
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Takahiro Okabe 《Journal of Differential Equations》2018,264(2):728-754
We consider the space-time behavior of the two dimensional Navier–Stokes flow. Introducing some qualitative structure of initial data, we succeed to derive the first order asymptotic expansion of the Navier–Stokes flow without moment condition on initial data in . Moreover, we characterize the necessary and sufficient condition for the rapid energy decay as motivated by Miyakawa–Schonbek [21]. By weighted estimated in Hardy spaces, we discuss the possibility of the second order asymptotic expansion of the Navier–Stokes flow assuming the first order moment condition on initial data. Moreover, observing that the Navier–Stokes flow lies in the Hardy space for , we consider the asymptotic expansions in terms of Hardy-norm. Finally we consider the rapid time decay as with cyclic symmetry introduced by Brandolese [2]. 相似文献
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Under the assumption that , we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrödinger operators in with periodic and antiperiodic boundary conditions to possess a Riesz basis of root vectors (i.e., eigenvectors and generalized eigenvectors spanning the range of the Riesz projection associated with the corresponding periodic and antiperiodic eigenvalues).We also discuss the case of a Schauder basis for periodic and antiperiodic Schrödinger operators in , . 相似文献
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