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In this paper, we give a new proof of a result of R. Jones showing almost everywhere convergence of spherical means of actions of Rd on Lp(X)-spaces are convergent for d?3 and p>d/(d-1). 相似文献
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This paper treats some variational principles for solutions of inhomogeneous p -Laplacian boundary value problems on exterior regions U?RN with dimension N?3. Existence-uniqueness results when p∈(1,N) are provided in a space E1,p(U) of functions that contains W1,p(U). Functions in E1,p(U) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an Lp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained. 相似文献
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Given a rank-r binary matroid we construct a system of O(r3) linear equations in O(r2) variables that has a solution over GF(2) if and only if the matroid is graphic. 相似文献
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We study the problem (−Δ)su=λeu in a bounded domain Ω⊂Rn, where λ is a positive parameter. More precisely, we study the regularity of the extremal solution to this problem. Our main result yields the boundedness of the extremal solution in dimensions n≤7 for all s∈(0,1) whenever Ω is, for every i=1,...,n, convex in the xi-direction and symmetric with respect to {xi=0}. The same holds if n=8 and s?0.28206..., or if n=9 and s?0.63237.... These results are new even in the unit ball Ω=B1. 相似文献
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For a non-degenerate convex subset Y of the n -dimensional Euclidean space Rn, let F(Y) be the family of all fuzzy sets of Rn which are upper semicontinuous, fuzzy convex and normal with compact supports contained in Y . We show that the space F(Y) with the topology of sendograph metric is homeomorphic to the separable Hilbert space ?2 if Y is compact; and the space F(Rn) is also homeomorphic to ?2. 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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Mohamed Ali Toumi 《Expositiones Mathematicae》2010,28(3):269-275
Let A be an Archimedean f -algebra and let N(A) be the set of all nilpotent elements of A. Colville et al. [4] proved that a positive linear map d:A→A is a derivation if and only if d(A)⊂N(A) and d(A2)={0}, where A2 is the set of all products ab in A. 相似文献
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In this paper, we consider the problem (Pε) : Δ2u=un+4/n-4+εu,u>0 in Ω,u=Δu=0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n>8 and ε>0. We analyze the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev inequality as ε→0 and we prove existence of solutions to (Pε) which blow up and concentrate around a critical point of the Robin's function. Finally, we show that for ε small, (Pε) has at least as many solutions as the Ljusternik–Schnirelman category of Ω. 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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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 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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Let K be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L∞(K) and C0(K), the class of left translation invariant w?-subalgebras of L∞(K) and finally the class of non-zero left translation invariant C?-subalgebras of C0(K) in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant w?-subalgebras of L∞(K), and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C?-subalgebras of C0(K). By the help of these two characterizations, we extract some results about invariant complemented subspaces of L∞(K) and C0(K). 相似文献
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Cristian Enache 《Comptes Rendus Mathematique》2014,352(1):37-42
In this note we derive a maximum principle for an appropriate functional combination of u(x) and |∇u|2, where u(x) is a strictly convex classical solution to a general class of Monge–Ampère equations. This maximum principle is then employed to establish some isoperimetric inequalities of interest in the theory of surfaces of constant Gauss curvature in RN+1. 相似文献