共查询到20条相似文献,搜索用时 46 毫秒
1.
We exhibit balance conditions between a Young function A and a Young function B for a Korn type inequality to hold between the LB norm of the gradient of vector-valued functions and the LA norm of its symmetric part. In particular, we extend a standard form of the Korn inequality in Lp, with 1<p<∞, and an Orlicz version involving a Young function A satisfying both the Δ2 and the ∇2 condition. 相似文献
2.
Jean-Stéphane Dhersin Fabian Freund Arno Siri-Jégousse Linglong Yuan 《Stochastic Processes and their Applications》2013
In this paper, we consider Beta(2−α,α) (with 1<α<2) and related Λ-coalescents. If T(n) denotes the length of a randomly chosen external branch of the n-coalescent, we prove the convergence of nα−1T(n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ(n) of collisions which occur in the n-coalescent until the end of the chosen external branch, and for the block counting process associated with the n-coalescent. 相似文献
3.
We give conditions on the kernel function (or activation function) for the family of radial basis function (RBF) neural networks obtained upon replacing the usual translation by the Delsarte one, with not necessarily the same smoothing factor in all kernel nodes, to have the universal approximation property in suitable weighted Lp-spaces (1?p<∞). A complete characterization of such kernels for p=1 and p=2 is provided. 相似文献
4.
We discuss joint temporal and contemporaneous aggregation of N independent copies of AR(1) process with random-coefficient a∈[0,1) when N and time scale n increase at different rate. Assuming that a has a density, regularly varying at a=1 with exponent −1<β<1, different joint limits of normalized aggregated partial sums are shown to exist when N1/(1+β)/n tends to (i) ∞, (ii) 0, (iii) 0<μ<∞. The limit process arising under (iii) admits a Poisson integral representation on (0,∞)×C(R) and enjoys ‘intermediate’ properties between fractional Brownian motion limit in (i) and sub-Gaussian limit in (ii). 相似文献
5.
We consider families of Ehrenfest chains and provide a simple criterion on the Lp-cutoff and the Lp-precutoff with specified initial states for 1≤p<∞. For the family with an Lp-cutoff, a cutoff time is described and a possible window is given. For the family without an Lp-precutoff, the exact order of the Lp-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity. 相似文献
6.
7.
A Banach lattice E is called p-disjointly homogeneous , 1≤p≤∞, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of ?p. Employing methods from interpolation theory, we clarify which r.i. spaces on [0,1] are p -disjointly homogeneous. In particular, for every 1<p<∞ and any increasing concave function φ on [0,1], which is not equivalent to neither 1 nor t, there exists a p-disjointly homogeneous r.i. space with the fundamental function φ . Moreover, it is shown that given 1<p<∞ and an increasing concave function φ with non-trivial dilation indices, there is a unique p-disjointly homogeneous space among all interpolation spaces between the Lorentz and Marcinkiewicz spaces associated with φ. 相似文献
8.
In this article, an existence theorem of global solutions with small initial data belonging to L1∩Lp, (n<p?∞) for a chemotaxis system is given on the whole space Rn, n?3. In the case p=∞, our global solution is integrable with respect to the space variable on some time interval, and then conserves the mass for a short time, at least. The system consists of a chemotaxis equation with a logarithmic term and an ordinary equation without diffusion term. 相似文献
9.
By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
10.
Let x(s), s∈Rd be a Gaussian self-similar random process of index H. We consider the problem of log-asymptotics for the probability pT that x(s), x(0)=0 does not exceed a fixed level in a star-shaped expanding domain T⋅Δ as T→∞. We solve the problem of the existence of the limit, θ?lim(−logpT)/(logT)D, T→∞, for the fractional Brownian sheet x(s), s∈[0,T]2 when D=2, and we estimate θ for the integrated fractional Brownian motion when D=1. 相似文献
11.
For Ω, an open bounded subset of RN with smooth boundary and 1<p<∞, we establish W1,p(Ω)a priori bounds and prove the compactness of solution sets to differential inequalities of the form which are bounded in L∞(Ω). The main point in this work is that the nonlinear term F may depend on ∇u and may grow as fast as a power of order p in this variable. Such growth conditions have been used extensively in the study of boundary value problems for nonlinear ordinary differential equations and are known as Bernstein–Nagumo growth conditions. In addition, we use these results to establish a sub-supersolution theorem. 相似文献
|divA(x,∇u)|≤F(x,u,∇u),
12.
In a rapidly growing population one expects that two individuals chosen at random from the nth generation are unlikely to be closely related if n is large. In this paper it is shown that for a broad class of rapidly growing populations this is not the case. For a Galton–Watson branching process with an offspring distribution {pj} such that p0=0 and ψ(x)=∑jpjI{j≥x} is asymptotic to x−αL(x) as x→∞ where L(⋅) is slowly varying at ∞ and 0<α<1 (and hence the mean m=∑jpj=∞) it is shown that if Xn is the generation number of the coalescence of the lines of descent backwards in time of two randomly chosen individuals from the nth generation then n−Xn converges in distribution to a proper distribution supported by N={1,2,3,…}. That is, in such a rapidly growing population coalescence occurs in the recent past rather than the remote past. We do show that if the offspring mean m satisfies 1<m≡∑jpj<∞ and p0=0 then coalescence time Xn does converge to a proper distribution as n→∞, i.e., coalescence does take place in the remote past. 相似文献
13.
We examine the regularity of weak solutions of quasi-geostrophic (QG) type equations with supercritical (α<1/2) dissipation α(−Δ). This study is motivated by a recent work of Caffarelli and Vasseur, in which they study the global regularity issue for the critical (α=1/2) QG equation [L. Caffarelli, A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, arXiv: math.AP/0608447, 2006]. Their approach successively increases the regularity levels of Leray–Hopf weak solutions: from L2 to L∞, from L∞ to Hölder (Cδ, δ>0), and from Hölder to classical solutions. In the supercritical case, Leray–Hopf weak solutions can still be shown to be L∞, but it does not appear that their approach can be easily extended to establish the Hölder continuity of L∞ solutions. In order for their approach to work, we require the velocity to be in the Hölder space C1−2α. Higher regularity starting from Cδ with δ>1−2α can be established through Besov space techniques and will be presented elsewhere [P. Constantin, J. Wu, Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press]. 相似文献
14.
In this paper we establish the boundedness of the extremal solution u∗ in dimension N=4 of the semilinear elliptic equation −Δu=λf(u), in a general smooth bounded domain Ω⊂RN, with Dirichlet data u|∂Ω=0, where f is a C1 positive, nondecreasing and convex function in [0,∞) such that f(s)/s→∞ as s→∞. 相似文献
15.
Félix Cabello Sánchez Jesús M.F. Castillo Jesús Suárez 《Nonlinear Analysis: Theory, Methods & Applications》2012
We show that c0 is the only Banach space with unconditional basis that satisfies the equation Ext(X,X)=0. This partially improves an old result by Kalton and Peck. We prove that the Kalton–Peck maps are strictly singular on a number of sequence spaces, including ?p for 0<p<∞, Tsirelson and Schlumprecht spaces and their duals, as well as certain super-reflexive variations of these spaces. In the last section, we give estimates of the projection constants of certain finite-dimensional twisted sums of Kalton–Peck type. 相似文献
16.
We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H. Integration is carried out over [0,t], t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t], t>0. 相似文献
17.
It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂Rd with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L2(Λ), H−1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established. 相似文献
18.
19.
20.
For a general subcritical second-order elliptic operator P in a domain Ω⊂Rn (or noncompact manifold), we construct Hardy-weight W which is optimal in the following sense. The operator P−λW is subcritical in Ω for all λ<1, null-critical in Ω for λ=1, and supercritical near any neighborhood of infinity in Ω for any λ>1. Moreover, if P is symmetric and W>0, then the spectrum and the essential spectrum of W−1P are equal to [1,∞), and the corresponding Agmon metric is complete. Our method is based on the theory of positive solutions and applies to both symmetric and nonsymmetric operators. The constructed Hardy-weight is given by an explicit simple formula involving two distinct positive solutions of the equation Pu=0, the existence of which depends on the subcriticality of P in Ω. 相似文献