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901.
For any , a truncated symmetric α-stable process is a symmetric Lévy process in with a Lévy density given by for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality
for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions
which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for
which the boundary Harnack principle fails.
The research of Panki Kim is supported by Research Settlement Fund for the new faculty of Seoul National University. The research
of Renming Song is supported in part by a joint US-Croatia grant INT 0302167. 相似文献
902.
We establish sufficient conditions for a cohomology class of a discrete subgroup Γ of a connected semisimple Lie group with finite center to be representable by a bounded differential form on the quotient by Γ of the associated symmetric space; furthermore if \(\rho : \Gamma\to\mathrm{PU}(1,q)\) is any representation of any discrete subgroup Γ of SU (1, p), we give an explicit closed bounded differential form on the quotient by Γ of complex hyperbolic space which is a representative for the pullback via ρ of the Kähler class of PU(1,q). If G,G′ are Lie groups of Hermitian type, we generalize to representations \(\rho : \Gamma\to G'\) of lattices Γ < G the invariant defined in [Burger, M., Iozzi, A.: Bounded cohomology and representation variates in PU (1,n). Preprint announcement, April 2000] for which we establish a Milnor–Wood type inequality. As an application we study maximal representations into PU(1, q) of lattices in SU(1,1). 相似文献
903.
Holger Dette Lorens A. Imhof 《Transactions of the American Mathematical Society》2007,359(10):4999-5018
We derive strong uniform approximations for the eigenvalues in general Laguerre and Hermite -ensembles by showing that the maximal discrepancy between the suitably scaled eigenvalues and roots of orthogonal polynomials converges almost surely to zero when the dimension converges to infinity. We also provide estimates of the rate of convergence. In the special case of a normalized real Wishart matrix , where denotes the dimension and the degrees of freedom, the rate is , if with , and the rate is , if with . In the latter case we also show the a.s. convergence of the largest eigenvalue of to the corresponding quantile of the Marcenko-Pastur law.
904.
Alexander Bendikov Patrick Maheux 《Transactions of the American Mathematical Society》2007,359(7):3085-3097
Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator , we prove a Nash type inequality for the fractional powers of . Under some assumptions, we give ultracontractivity bounds for the semigroup generated by .
905.
This paper is devoted to discuss the regularity of the weak solution to a class of non-linear equations corresponding to Hardy-Sobolev
type inequality on the H-type group. Combining the Serrin's idea and the Moser's iteration, Lp estimates of the weak solution are obtained, which generalize the results of Garofalo and Vassilev in [6, 14]. As an application,
asymptotic behavior of the weak solution has been discussed. Finally, doubling property and unique continuation of the weak
solution are given.
*This material is based upon work funded by Zhejiang Provincial Natural Science Foundation of China under Grant No. Y606144. 相似文献
906.
塑性全量理论的变分不等式模式及其无迭代解 总被引:1,自引:0,他引:1
变分不等式是解决一类带单侧约束的定常力学问题的有效数学工具.本文就弹塑性全量理论构造了等价的变分不等式模式,解除了弹塑性问题本构约束的不等式关系,比一般能量形式的描述更为简洁.它便于计算,具有可靠的数学依据,可以用二次规划法求解.计算时无需分级加载迭代,一步即可得收敛解. 相似文献
907.
The Hölder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case 1
相似文献
908.
王颖坚 《应用数学和力学(英文版)》1990,11(4):343-353
Basic equations for large deflection theory of thin orthotropic circular plate with variable thickness are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure. If ε=0, then the solution derived from the result in this paper coincides completely with the result given by J. Nowinski (using perturbation method) for solving large deflection problem of thin orthotropic circular plate with constant thickness under uniform pressure. 相似文献
909.
张祥 《应用数学和力学(英文版)》1990,11(11):1067-1074
In this paper,we consider the vector nonlinear boundary value problem:εy~v=f(x,y,z,y′,ε),y(0)=A_1,y(1)=B_1εz~v=g(x,y,z,z′,ε),z(0)=A_2,z(1)=B_2whereε>0 is a small parameter,0≤x≤1 ,f and g are continuous functions in R~4,Under appropriate assumptions,by means of the differential inequalities,we demonstratethe existence and estimation,involving boundary and interior layers,of the solutions to theabove problem. 相似文献
910.
Recently,many authors have generalized the famous Ky Fan’s minimaxinequality.In this paper,we put forward T-diagonal convexity(concavity)conditions anddevelop the main results in this respect.Next.we discuss some fixed point problems,andgeneralize the Fan-Glicksberg’s fixed point theorem. 相似文献