共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in are obtained by introducing a new linearized system with respect to for constants and , and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of in norm. 相似文献
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Carme Cascante Joan Fàbrega Joaquín M. Ortega 《Journal of Mathematical Analysis and Applications》2018,457(1):722-750
In this paper we characterize the boundedness of the bilinear form defined by in the product of homogeneous Sobolev spaces , . We deduce a characterization of the space of pointwise multipliers from to its dual in terms of trace measures. 相似文献
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Let be the -dimensional complex projective space, and let be two non-empty open subsets of in the Zariski topology. A hypersurface in induces a bipartite graph as follows: the partite sets of are and , and the edge set is defined by if and only if . Motivated by the Turán problem for bipartite graphs, we say that is -grid-free provided that contains no complete bipartite subgraph that has vertices in and vertices in . We conjecture that every -grid-free hypersurface is equivalent, in a suitable sense, to a hypersurface whose degree in is bounded by a constant , and we discuss possible notions of the equivalence.We establish the result that if is -grid-free, then there exists of degree in such that . Finally, we transfer the result to algebraically closed fields of large characteristic. 相似文献
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A vector field in is said to be harmonic in the open set U if , in U. Harmonic vector fields are a natural extension to of the concept of analytic function of complex variable. We characterize continuous linear functionals acting on the space of germs of harmonic vector fields on a compact set K. This result provides an -analog of a theorem by G. Köthe on the dual of the space of germs of analytic functions of complex variable on a compact. To cite this article: R. Dáger, A. Presa, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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Masoud Hassani 《Comptes Rendus Mathematique》2017,355(11):1133-1137
In this paper, we study the irreducible representation of in . This action preserves a quadratic form with signature . Thus, it acts conformally on the 3-dimensional Einstein universe . We describe the orbits induced in and its complement in . This work completes the study in [2], and is one element of the classification of cohomogeneity one actions on [5]. 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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Let be an isometric immersion from a Riemannian n-manifold into a Euclidean m-space. Denote by Δ and the Laplace operator and the position vector of M, respectively. Then M is called biharmonic if . The following Chen?s Biharmonic Conjecture made in 1991 is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper we prove that the biharmonic conjecture is true for -ideal and -ideal hypersurfaces of a Euclidean space of arbitrary dimension. 相似文献
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Let be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ?Ω. We show that the solution to the linear first-order system:(1) vanishes if and . In particular, square-integrable solutions ζ of (1) with vanish. As a consequence, we prove that: is a norm if with , for some with as well as . We also give a new and different proof for the so-called ‘infinitesimal rigid displacement lemma’ in curvilinear coordinates: Let , , satisfy for some with . Then there exists a constant translation vector and a constant skew-symmetric matrix , such that . 相似文献