共查询到20条相似文献,搜索用时 15 毫秒
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TheImprovementofFischer'sInequalityandHadamard'sInequalityHuangLiping(黄礼平)(DepartmentofBasicSciences,XiangtanMiningInstitute,... 相似文献
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For β ∈ R, the authors consider the evolution system in the unknown variables u and α { ttu+ xxxxu+ xxtα+(β+|| xu||L2^2) xxu=f, ttα- xxα- xxtα- xxtu=0} describing the dynamics of type III thermoelastic extensible beams, where the dissipation is entirely contributed by the second equation ruling the evolution of the thermal displacement α. Under natural boundary conditions, the existence of the global attractor of optimal regularity for the related dynamical system acting on the phase space of weak energy solutions is established. 相似文献
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S. Dar 《Geometriae Dedicata》1999,77(1):1-9
We formulate and discuss a conjecture that might strengthen the Brunn–Minkowski inequality. 相似文献
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Philippe G. CIARLET 《数学年刊B辑(英文版)》2010,31(5):607-618
Two models based on the hydrostatic primitive equations are proposed. The first model is the primitive equations with partial viscosity only, and is oriented towards large-scale wave structures in the ocean and atmosphere. The second model is the viscous primitive equations with spectral eddy viscosity, and is oriented towards turbulent geophysical flows. For both models, the existence and uniqueness of global strong solutions are established. For the second model, the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established. 相似文献
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We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is connected to an old result of Mahler concerning the the measure of a convex body and its geometric polar being essentially reciprocal. An additional assumption, that the weights must belong to a reverse Hölder class, is used to formulate the sufficient condition. 相似文献
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Recently, Dhongade and Yeh studied some integral inequalities in R and R~n respectively, we find that their work can be improved. In this paper, we will improve their results, one of our results is best, i.e. it can not be improved again, another of our results is better than Yeh's. 相似文献
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In this paper, we improve an inequality of Vinogradov by analysis method. 相似文献
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We prove a sharp Alexandrov–Fenchel-type inequality for star-shaped, strictly mean convex hypersurfaces in hyperbolic n-space, n ≥ 3. The argument uses two new monotone quantities along the inverse mean curvature flow. As an application we establish, in any dimension, an optimal Penrose inequality for asymptotically hyperbolic graphs carrying a minimal horizon, with the equality occurring if and only if the graph is an anti-de Sitter–Schwarzschild solution. This sharpens previous results by Dahl–Gicquaud–Sakovich and settles, for this class of initial data sets, the conjectured Penrose inequality for time-symmetric space–times with negative cosmological constant. We also explain how our methods can be easily adapted to derive an optimal Penrose inequality for asymptotically locally hyperbolic graphs in any dimension n ≥ 3. When the horizon has the topology of a compact surface of genus at least one, this provides an affirmative answer, for this class of initial data sets, to a question posed by Gibbons, Chru?ciel and Simon on the validity of a Penrose-type inequality for exotic black holes. 相似文献
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It was proved by R. Gomory and T. Hu in 1961 that, for every finite nonempty ultrametric space (X, d), the inequaliy \( \left| {\mathrm{Sp}(X)} \right|\leq \left| X \right|-1 \), where Sp(X) = {d(x, y) : x, y ∈ X, x ≠ y} , holds. We characterize the spaces X for which the equality is attained by the structural properties of some graphs and show that the set of isometric types of such X is dense in the Gromov–Hausdorff space of the isometric types of compact ultrametric spaces. 相似文献
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OnanInequalityofJenkinsType¥WeiHanbai(InstituteofMathematics,FudanUniversity,Shanghai,200433,P.R.C)Abstract:Inthispeper,theau... 相似文献
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A. Boulkhemair 《偏微分方程通讯》2013,38(9):1439-1447
We give a proof of the Poincaré inequality in W 1, p (Ω) with a constant that is independent of Ω ? , where is a set of uniformly bounded and uniformly Lipschitz domains in ? n . As a byproduct, we obtain the following: The first non vanishing eigenvalues λ2(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the domains Ω vary and remain uniformly bounded and uniformly Lipschitz regular. 相似文献
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In this paper, we find the largest contant C such that sin2 x xtanx > 2x2 cx5tan x 0相似文献
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An Interpolation of Hardy Inequality and Moser–Trudinger Inequality on Riemannian Manifolds with Negative Curvature
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Let M be a complete, simply connected Riemannian manifold with negative curvature.We obtain an interpolation of Hardy inequality and Moser–Trudinger inequality on M. Furthermore,the constant we obtain is sharp. 相似文献
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We establish Talagrand's T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type's approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction-Diffusion equations are provided. 相似文献
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Long JIANG Department of Mathematics China University of Mining Technology Xuzhou Jiangsu China School of Mathematical Sciences Fudan University Shanghai China School of Mathematics System Sciences Shandong University Jinan China. 《数学年刊B辑(英文版)》2006,27(5)
Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen's inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) = 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen's inequality for g-expectation in [4, 7-9]. 相似文献
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Yuqiao LI 《数学年刊B辑(英文版)》2022,43(1):115-124
The author proves that the isoperimetric inequality on the graphic curves over circle or hyperplanes over Sn-1is satisfied in the cigar steady soliton and in the Bryant steady soliton. Since both of them are Riemannian manifolds with warped product metric,the author utilize the result of Guan-Li-Wang to get his conclusion. For the sake of the soliton structure, the author believes that the geometric restrictions for manifolds in which the isoperimetric inequality holds are naturally s... 相似文献
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Biharmonic Equation and an Improved Hardy Inequality 总被引:6,自引:0,他引:6
Yang-xinYao Yao-tianShen Zhi-huiChen 《应用数学学报(英文版)》2004,20(3):433-440
An improved Hardy inequality will be proven in the present work.Using the improved Hardy in-equality and variational techniques,we also discuss the existence of nontrivial solution for following the weightedeigenvalue problem:(?) 相似文献