共查询到20条相似文献,搜索用时 10 毫秒
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We prove new weighted Hardy type inequalities with sharp constants and describe their applications to inequalities in multidimensional domains. 相似文献
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In this paper, we analyze solutions of the open Toda system and establish an optimal Moser‐Trudinger type inequality for this system. Let Σ be a closed surface with area 1 and K = (aij)N × N the Cartan matrix for SU(N + 1), i.e., We show that has a lower bound in (H1(Σ))N if and only if This inequality is optimal. As a direct consequence, if Mj < for 4π for j = 1, 2, …, N, ΦM has a minimizer u that satisfies © 2001 John Wiley & Sons, Inc. 相似文献
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Tianling Jin Jingang Xiong 《Calculus of Variations and Partial Differential Equations》2013,48(3-4):555-585
In this paper, we establish some sharp weighted trace inequalities ${W^{1,2}(\rho^{1-2 \sigma}, M) \hookrightarrow L^{\frac{2n}{n-2 \sigma}}(\partial M)}$ on n + 1 dimensional compact smooth manifolds with smooth boundaries, where ρ is a defining function of M and ${\sigma \in (0,1)}$ . This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin. 相似文献
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Mathematical Notes - 相似文献
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Dimitar K. Dimitrov Vladimir P. Kostov 《Journal of Mathematical Analysis and Applications》2011,376(2):385-392
We present new sharp inequalities for the Maclaurin coefficients of an entire function from the Laguerre-Pólya class. They are obtained by a new technique involving the so-called very hyperbolic polynomials. The results may be considered as extensions of the classical Turán inequalities. 相似文献
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For every metric space (X, d) and origin o ∈ X, we show the inequality I o (x, y) ≤ 2d o (x, y), where I o (x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o , and x, y ∈ X \ {o} The constant 2 is best possible. 相似文献
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Van Hoang Nguyen 《Journal of Functional Analysis》2021,280(3):108833
In this paper, we prove the existence of maximizers for the sharp Moser–Trudinger type inequalities in whole space , with more general nonlinearity. The main key in our proof is a precise estimate of the concentrating level of the Moser–Trudinger functional associated with our inequalities on the normalized concentrating sequences. This estimate solves a heavily non-trivial and open problem related to the sharp Moser–Trudinger inequality. Our method gives an alternative proof of the existence of maximizers for the Moser–Trudinger inequality and singular Moser–Trudinger inequality in whole space due to Li and Ruf [30] and Li and Yang [31] without using blow-up analysis argument. 相似文献
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Martin Fuchs 《Mathematical Methods in the Applied Sciences》2011,34(15):1920-1932
We collect various Poincaré‐type inequalities valid for fields of bounded deformation and give explicit upper bounds for the constants being involved. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Consider the following inequalities due to Caffarelli, Kohn, and Nirenberg [6] where, for N ≥ 3, −∞ < a < (N − 2)/2, a ≤ b ≤ a + 1, and p = 2N/(N − 2 + 2(b − a)). We shall answer some fundamental questions concerning these inequalities such as the best embedding constants, the existence and nonexistence of extremal functions, and their qualitative properties. While the case a ≥ 0 has been studied extensively and a complete solution is known, little has been known for the case a < 0. Our results for the case a < 0 reveal some new phenomena which are in striking contrast with those for the case a ≥ 0. Results for N = 1 and N = 2 are also given. © 2001 John Wiley & Sons, Inc. 相似文献
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Xianghong Gong 《Mathematische Annalen》1997,309(4):611-623
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Yaning Wang 《Mathematische Nachrichten》2021,294(1):195-206
Let M be a Hopf hypersurface in a nonflat complex space form , , of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces of dimension three. By means of this result, we give some new characterizations of Hopf hypersurfaces of type (A) and (B) which generalize those in [14, 18, 26]. 相似文献
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Emmanuel Hebey 《Transactions of the American Mathematical Society》2002,354(3):1193-1213
Given a smooth compact Riemannian -manifold, , we return in this article to the study of the sharp Sobolev-Poincaré type inequality
where is the critical Sobolev exponent, and is the sharp Euclidean Sobolev constant. Druet, Hebey and Vaugon proved that is true if , that is true if and the sectional curvature of is a nonpositive constant, or the Cartan-Hadamard conjecture in dimension is true and the sectional curvature of is nonpositive, but that is false if and the scalar curvature of is positive somewhere. When is true, we define as the smallest in . The saturated form of reads as
We assume in this article that , and complete the study by Druet, Hebey and Vaugon of the sharp Sobolev-Poincaré inequality . We prove that is true, and that possesses extremal functions when the scalar curvature of is negative. A fairly complete answer to the question of the validity of under the assumption that the scalar curvature is not necessarily negative, but only nonpositive, is also given.
where is the critical Sobolev exponent, and is the sharp Euclidean Sobolev constant. Druet, Hebey and Vaugon proved that is true if , that is true if and the sectional curvature of is a nonpositive constant, or the Cartan-Hadamard conjecture in dimension is true and the sectional curvature of is nonpositive, but that is false if and the scalar curvature of is positive somewhere. When is true, we define as the smallest in . The saturated form of reads as
We assume in this article that , and complete the study by Druet, Hebey and Vaugon of the sharp Sobolev-Poincaré inequality . We prove that is true, and that possesses extremal functions when the scalar curvature of is negative. A fairly complete answer to the question of the validity of under the assumption that the scalar curvature is not necessarily negative, but only nonpositive, is also given.
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Lagrangian submanifolds appear naturally in the context of classical mechanics. Moreover, they play some important roles in supersymmetric field theories as well as in string theory. In this paper we establish general inequalities for Lagrangian submanifolds in complex space forms. We also provide examples showing that these inequalities are the best possible. Moreover, we provide simple non-minimal examples which satisfy the equality case of the improved inequalities. 相似文献
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V. V. Volchkov 《Ukrainian Mathematical Journal》1995,47(1):125-129
The exact dependence of constants in Jackson-type inequalities on the rate of convergence of the Diophantine approximations of certain numbers is obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 108–110, January, 1995. 相似文献