共查询到20条相似文献,搜索用时 31 毫秒
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We prove various Hardy-type and uncertainty inequalities on a stratified Lie group G . In particular, we show that the operators Tα:f?|⋅|−αL−α/2f, where |⋅| is a homogeneous norm, 0<α<Q/p, and L is the sub-Laplacian, are bounded on the Lebesgue space Lp(G). As consequences, we estimate the norms of these operators sufficiently precisely to be able to differentiate and prove a logarithmic uncertainty inequality. We also deduce a general version of the Heisenberg–Pauli–Weyl inequality, relating the Lp norm of a function f to the Lq norm of |⋅|βf and the Lr norm of Lδ/2f. 相似文献
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The dimension of a point x in Euclidean space (meaning the constructive Hausdorff dimension of the singleton set {x}) is the algorithmic information density of x . Roughly speaking, this is the least real number dim(x) such that r×dim(x) bits suffice to specify x on a general-purpose computer with arbitrarily high precision 2−r. The dimension spectrum of a set X in Euclidean space is the subset of [0,n] consisting of the dimensions of all points in X. 相似文献
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We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α<1/2) dissipation α(−Δ): If a Leray–Hopf weak solution is Hölder continuous θ∈Cδ(R2) with δ>1−2α on the time interval [t0,t], then it is actually a classical solution on (t0,t]. 相似文献
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João Marcos do Ó Manassés de SouzaEveraldo de Medeiros Uberlandio Severo 《Journal of Differential Equations》2014
In line with the Concentration–Compactness Principle due to P.-L. Lions [19], we study the lack of compactness of Sobolev embedding of W1,n(Rn), n?2, into the Orlicz space LΦα determined by the Young function Φα(s) behaving like eα|s|n/(n−1)−1 as |s|→+∞. In the light of this result we also study existence of ground state solutions for a class of quasilinear elliptic problems involving critical growth of the Trudinger–Moser type in the whole space Rn. 相似文献
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Jean-Pierre Kahane 《Comptes Rendus Mathematique》2014,352(5):383-385
For almost all x>1, (xn)(n=1,2,…) is equidistributed modulo 1, a classical result. What can be said on the exceptional set? It has Hausdorff dimension one. Much more: given an (bn) in [0,1[ and ε>0, the x -set such that |xn−bn|<ε modulo 1 for n large enough has dimension 1. However, its intersection with an interval [1,X] has a dimension <1, depending on ε and X. Some results are given and a question is proposed. 相似文献
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We show that for any δ∈[0,1) there exists a homogeneous order 2−δ analytic outside zero solution to a uniformly elliptic Hessian equation in R5. 相似文献
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Rolci Cipolatti Flávio Dickstein Jean-Pierre Puel 《Journal of Mathematical Analysis and Applications》2015
We study the existence of standing wave solutions of the complex Ginzburg–Landau equation in RN, where α>0, (N−2)α<4, ρ>0 and θ,γ∈R. We show that for any θ∈(−π/2,π/2) there exists ε>0 such that (GL) has a non-trivial standing wave solution if |γ−θ|<ε. Analogous result is obtained in a ball Ω∈RN for ρ>−λ1, where λ1 is the first eigenvalue of the Laplace operator with Dirichlet boundary conditions. 相似文献
equation(GL)
φt−eiθ(ρI−Δ)φ−eiγ|φ|αφ=0
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Recently, Alfakih and Ye (2013) [4] proved that if an r -dimensional bar framework (G,p) on n?r+2 nodes in general position in Rr admits a positive semidefinite stress matrix with rank n−r−1, then (G,p) is universally rigid. In this paper, we generalize this result in two directions. First, we extend this result to tensegrity frameworks. Second, we replace the general position assumption by the weaker assumption that in configuration p, each point and its neighbors in G affinely span Rr. 相似文献
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Let P(D) be a nonnegative homogeneous elliptic operator of order 2m with real constant coefficients on Rn and V be a suitable real measurable function. In this paper, we are mainly devoted to establish the Gaussian upper bound for Schrödinger type semigroup e−tH generated by H=P(D)+V with Kato type perturbing potential V , which naturally generalizes the classical result for Schrödinger semigroup e−t(Δ+V) as V∈K2(Rn), the famous Kato potential class. Our proof significantly depends on the analyticity of the free semigroup e−tP(D) on L1(Rn). As a consequence of the Gaussian upper bound, the Lp-spectral independence of H is concluded. 相似文献
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In this paper the question of finding infinitely many solutions to the problem −Δu+a(x)u=|u|p−2u, in RN, u∈H1(RN), is considered when N≥2, p∈(2,2N/(N−2)), and the potential a(x) is a positive function which is not required to enjoy symmetry properties. Assuming that a(x) satisfies a suitable “slow decay at infinity” condition and, moreover, that its graph has some “dips”, we prove that the problem admits either infinitely many nodal solutions or infinitely many constant sign solutions. The proof method is purely variational and allows to describe the shape of the solutions. 相似文献
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For an algebraically closed field F, we show that any matrix polynomial P(λ)∈F[λ]n×m, n?m, can be reduced to triangular form, preserving the degree and the finite and infinite elementary divisors. We also characterize the real matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal blocks of sizes 1×1 and 2×2. The proofs we present solve the structured inverse problem of building up triangular matrix polynomials starting from lists of elementary divisors. 相似文献