查看更多>>摘要：For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic deriva-tives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.
查看更多>>摘要：This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation△2u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B4,under the smallest regularity assumptions of V,(w),ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of bihar-monic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.
查看更多>>摘要：In this note,we mainly make use of a method devised by Shaw[15]for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω=(Ω)\(∪mj=1Ωj),where(Ω)and {Ωj }mj=1(∈)(Ω)are bounded pseudoconvex domains in Cn with smooth boundaries,and(Ω)1,…,(Ω)m are mutually disjoint.The main results can also be quickly obtained by virtue of[5].
查看更多>>摘要：In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak*-weak denting point and the weak*-weak*denting point of a set.These are the generalizations of the weak*denting point of a set in a dual Banach space.By use of the weak*-weak denting point,we characterize the very smooth space,the point of weak*-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.
查看更多>>摘要：In this article,we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials.It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation.We prove that any solution with mild regularity will become smooth in Gevrey class at positive time,with a sharp Gevrey index,depending on the angular singularity.Our proof relies on the elementary L2 weighted estimates.
查看更多>>摘要：In this paper,we investigate spacelike graphs defined over a domain Ω ⊂ Mn in the Lorentz manifold Mn × R with the metric-ds2+σ,where Mn is a complete Riemannian n-manifold with the metric σ,Ω has piecewise smooth boundary,and R denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in Mn × R under a conformal transformation.
查看更多>>摘要：Assume that L is a non-negative self-adjoint operator on L2(Rn)with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space on Rn satisfying some mild assumptions.Let HX,L(Rn)be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal func-tion characterizations of the Hardy space HX,L(Rn)and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function character-izations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.
查看更多>>摘要：This paper is mainly about the spectral properties of a class of Jacobi operators(Hc,bu)(n)=cnu(n+1)+cn-1u(n-1)+bnu(n),where |cn-1|=O(n-α)and bn=O(n-1).We will show that,for α ≥ 1,the singular continuous spectrum of the operator is empty.
查看更多>>摘要：Let n ≥ 2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in Rn.In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L1/2 satisfies the weighted Lp estimates ||L1/2(f)||Lpω(Rn)≤C||▽f||Lpω(Rn;Rn)for any p ∈(1,∞)and ω∈ Ap(Rn)(the class of Muckenhoupt weights),and that ||▽f||Lpω(Rn;Rn)≤ C||L1/2(f)||Lpω(Rn)for any p ∈(1,2+ε)and ω ∈ Ap(Rn)∩RH(2+ε/p)'(Rn)(the class of reverse Hölder weights),where e ∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q ∈(2,∞),we give a sufficient condition to obtain that||▽f||Lpω(Rn;Rn)≤ C||L1/2(f)||Lpω(Rn)for any p ∈(1,q)and ω ∈ Ap(Rn)∩ RH(q/p)'(Rn).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform ▽L-1/2 is bounded on Lpω(Rn)for any given p ∈(1,∞)and ω ∈ Ap(Rn).Furthermore,applications to the weighted L2-regularity problem with the Dirichlet or the Neumann boundary condition are also given.
查看更多>>摘要：This paper studies a strongly convergent inertial forward-backward-forward al-gorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.
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