共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we prove that if a sequence of homeomorphisms , with bounded planar domains, of Sobolev space has uniformly equibounded distortions in EXP(Ω) and weakly converges to f in then the matrices A(x, f
j
) of the corresponding Laplace-Beltrami operators Γ-converge in the Orlicz–Sobolev space , where Q(t) = t
2log(e + t), to the matrix A(x, f) of the Laplace-Beltrami operator associated to f.
相似文献
2.
A general result on precise asymptotics for linear processes of positively associated sequences 总被引:2,自引:0,他引:2
Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers satisfying ∑j=0^∞|aj|〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E|ε1|^2+δ′〈 for some δ′〉0 and μ(n)=O(n^-ρ) for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}. 相似文献
3.
Soogil Seo 《manuscripta mathematica》2008,127(3):381-396
A circular distribution is a Galois equivariant map ψ from the roots of unity μ
∞ to an algebraic closure of such that ψ satisfies product conditions, for ϵ ∈ μ
∞ and , and congruence conditions for each prime number l and with (l, s) = 1, modulo primes over l for all , where μ
l
and μ
s
denote respectively the sets of lth and sth roots of unity. For such ψ, let be the group generated over by and let be , where U
s
denotes the global units of . We give formulas for the indices and of and inside the circular numbers P
s
and units C
s
of Sinnott over .
This work was supported by the SRC Program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government
(MOST) (No. R11-2007-035-01001-0). This work was supported by the Korea Research Foundation Grant funded by the Korean Government
(MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00455). 相似文献
4.
We consider the generalized Gagliardo–Nirenberg inequality in in the homogeneous Sobolev space with the critical differential order s = n/r, which describes the embedding such as for all q with p ≦ q < ∞, where 1 < p < ∞ and 1 < r < ∞. We establish the optimal growth rate as q → ∞ of this embedding constant. In particular, we realize the limiting end-point r = ∞ as the space of BMO in such a way that with the constant C
n
depending only on n. As an application, we make it clear that the well known John–Nirenberg inequality is a consequence of our estimate. Furthermore,
it is clarified that the L
∞-bound is established by means of the BMO-norm and the logarithm of the -norm with s > n/r, which may be regarded as a generalization of the Brezis–Gallouet–Wainger inequality. 相似文献
5.
Peer Christian Kunstmann 《Archiv der Mathematik》2008,91(2):178-186
We consider the Stokes operator A on unbounded domains of uniform C
1,1-type. Recently, it has been shown by Farwig, Kozono and Sohr that – A generates an analytic semigroup in the spaces , 1 < q < ∞, where for q ≥ 2 and for q ∈ (1, 2). Moreover, it was shown that A has maximal L
p
-regularity in these spaces for p ∈ (1,∞). In this paper we show that ɛ + A has a bounded H
∞-calculus in for all q ∈ (1, ∞) and ɛ > 0. This allows to identify domains of fractional powers of the Stokes operator.
Received: 12 October 2007 相似文献
6.
Guang Yuan Zhang 《Mathematische Annalen》2007,337(2):401-433
Let Δ
n
be the ball |x| < 1 in the complex vector space
, let
be a holomorphic mapping and let M be a positive integer. Assume that the origin
is an isolated fixed point of both f and the Mth iteration f
M
of f. Then for each factor m of M, the origin is again an isolated fixed point of f
m
and the fixed point index
of f
m
at the origin is well defined, and so is the (local) Dold’s index [Invent. Math. 74(3), 419–435 (1983)] at the origin:
where P(M) is the set of all primes dividing M, the sum extends over all subsets τ of P(M), #τis the cardinal number of τ and
. P
M
( f,0) can be interpreted to be the number of periodic points of period M of f overlapped at the origin: any holomorphic mapping
sufficiently close to f has exactly P
M
( f,0) distinct periodic points of period M near the origin, provided that all the fixed points of
near the origin are simple. Note that f itself has no periodic point of period M near the origin if M > 1. According to Shub and Sullivan’s work [Topology 13, 189–191(1974)] a necessary condition so that P
M
( f,0) ≠ 0 is that the linear part of f at the origin has a periodic point of period M. The goal of this paper is to prove that this condition is sufficient as well for holomorphic mappings.Project 10271063 and 10571009 supported by NSFC 相似文献
7.
Second-order half-linear differential equation (H): on the finite interval I = (0,1] will be studied, where , p > 1 and the coefficient f(x) > 0 on I, , and . In case when p = 2, the equation (H) reduces to the harmonic oscillator equation (P): y′′ + f(x)y = 0. In this paper, we study the oscillations of solutions of (H) with special attention to some geometric and fractal properties of the graph . We establish integral criteria necessary and sufficient for oscillatory solutions with graphs having finite and infinite
arclength. In case when , λ > 0, α > p, we also determine the fractal dimension of the graph G(y) of the solution y(x). Finally, we study the L
p
nonintegrability of the derivative of all solutions of the equation (H).
相似文献
8.
B. P. Duggal 《Integral Equations and Operator Theory》2009,63(1):17-28
A Banach space operator T ∈ B(χ) is polaroid if points λ ∈ iso σ(T) are poles of the resolvent of T. Let denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower
semi–Fredholm spectrum of T. For A, B and C ∈ B(χ), let M
C
denote the operator matrix . If A is polaroid on , M
0 satisfies Weyl’s theorem, and A and B satisfy either of the hypotheses (i) A has SVEP at points and B has SVEP at points , or, (ii) both A and A* have SVEP at points , or, (iii) A* has SVEP at points and B
* has SVEP at points , then . Here the hypothesis that λ ∈ π0(M
C
) are poles of the resolvent of A can not be replaced by the hypothesis are poles of the resolvent of A.
For an operator , let . We prove that if A* and B* have SVEP, A is polaroid on π
a
0(M
C) and B is polaroid on π
a
0(B), then .
相似文献
9.
Jean-Christophe Bourgoin 《Annals of Global Analysis and Geometry》2007,32(1):1-13
In this paper, we study the minimality of the map for the weighted energy functional , where is a continuous function. We prove that for any integer and any non-negative, non-decreasing continuous function f, the map minimizes E
f,p
among the maps in which coincide with on . The case p = 1 has been already studied in [Bourgoin J.-C. Calc. Var. (to appear)]. Then, we extend results of Hong (see Ann. Inst.
Poincaré Anal. Non-linéaire 17: 35–46 (2000)). Indeed, under the same assumptions for the function f, we prove that in dimension n ≥ 7 for any real with , the map minimizes E
f,p
among the maps in which coincide with on .
相似文献
10.
In this paper we consider the Lane–Emden problem adapted for the p-Laplacian
where Ω is a bounded domain in , n ≥ 2, λ > 0 and p < q < p* (with if p < n, and p* = ∞ otherwise). After some recalls about the existence of ground state and least energy nodal solutions, we prove that,
when q → p, accumulation points of ground state solutions or of least energy nodal solutions are, up to a “good” scaling, respectively
first or second eigenfunctions of −Δ
p
.
Received: 29 April 2008 相似文献
11.
Let T and be arbitrary nonnegative, irreducible, stochastic matrices corresponding to two ergodic Markov chains on n states. A function κ is called a condition number for Markov chains with respect to the (α, β)–norm pair if . Here π and are the stationary distribution vectors of the two chains, respectively. Various condition numbers, particularly with respect
to the (1, ∞) and (∞, ∞)-norm pairs have been suggested in the literature. They were ranked according to their size by Cho
and Meyer in a paper from 2001. In this paper we first of all show that what we call the generalized ergodicity coefficient
, where e is the n-vector of all 1’s and A
# is the group generalized inverse of A = I − T, is the smallest condition number of Markov chains with respect to the (p, ∞)-norm pair. We use this result to identify the smallest condition number of Markov chains among the (∞, ∞) and (1, ∞)-norm
pairs. These are, respectively, κ
3 and κ
6 in the Cho–Meyer list of 8 condition numbers. Kirkland has studied κ
3(T). He has shown that and he has characterized transition matrices for which equality holds. We prove here again that 2κ
3(T) ≤ κ(6) which appears in the Cho–Meyer paper and we characterize the transition matrices T for which . There is actually only one such matrix: T = (J
n
− I)/(n − 1), where J
n
is the n × n matrix of all 1’s.
This research was supported in part by NSERC under Grant OGP0138251 and NSA Grant No. 06G–232. 相似文献
12.
Consider the instationary Navier–Stokes system in a smooth bounded domain with vanishing force and initial value . Since the work of Kiselev and Ladyzhenskaya (Am. Math. Soc. Transl. Ser. 2 24:79–106, 1963) there have been found several
conditions on u
0 to prove the existence of a unique strong solution with u(0) = u
0 in some time interval [0, T), 0 < T ≤ ∞, where the exponents 2 < s < ∞, 3 < q < ∞ satisfy . Indeed, such conditions could be weakened step by step, thus enlarging the corresponding solution classes. Our aim is to
prove the following optimal result with the weakest possible initial value condition and the largest possible solution class:
Given u
0, q, s as above and the Stokes operator A
2, we prove that the condition is necessary and sufficient for the existence of such a local strong solution u. The proof rests on arguments from the recently developed theory of very weak solutions. 相似文献
13.
Tord Sj?din 《manuscripta mathematica》2008,127(3):369-380
A theorem of Beurling states that if f satisfies , n = 1, 2,..., for some 0 < ρ < 2, on a real interval I, then f is analytic in a rhombus containing I. We study the corresponding problem for the quantum differences Δ
n
f (q, x), q > 1, n = 1, 2,..., for functions defined on (0, ∞) and prove quantitative and qualitative analogues of Beurling’s result. We also
characterize the analyticity of f on subintervals of (0, ∞) in q-analytic terms. 相似文献
14.
Let f : X → Y be a morphism of pure-dimensional schemes of the same dimension, with X smooth. We prove that if is an arc on X having finite order e along the ramification subscheme R
f
of X, and if its image δ = f
∞(γ) on Y does not lie in J
∞(Y
sing), then the induced map T
γ
J
∞(X) → T
δ
J
∞(Y) is injective, with a cokernel of dimension e. In particular, if Y is smooth too, and if we denote by and the formal neighborhoods of and , then the induced morphism is a closed embedding of codimension e.
相似文献
15.
Let M be a smooth compact oriented Riemannian manifold of dimension n without boundary, and let Δ be the Laplace–Beltrami operator on M. Say , and that f (0) = 0. For t > 0, let K
t
(x, y) denote the kernel of f (t
2 Δ). Suppose f satisfies Daubechies’ criterion, and b > 0. For each j, write M as a disjoint union of measurable sets E
j,k
with diameter at most ba
j
, and measure comparable to if ba
j
is sufficiently small. Take x
j,k
∈ E
j,k
. We then show that the functions form a frame for (I − P)L
2(M), for b sufficiently small (here P is the projection onto the constant functions). Moreover, we show that the ratio of the frame bounds approaches 1 nearly
quadratically as the dilation parameter approaches 1, so that the frame quickly becomes nearly tight (for b sufficiently small). Moreover, based upon how well-localized a function F ∈ (I − P)L
2 is in space and in frequency, we can describe which terms in the summation are so small that they can be neglected. If n = 2 and M is the torus or the sphere, and f (s) = se
−s
(the “Mexican hat” situation), we obtain two explicit approximate formulas for the φ
j,k
, one to be used when t is large, and one to be used when t is small.
A. Mayeli was partially supported by the Marie Curie Excellence Team Grant MEXT-CT-2004-013477, Acronym MAMEBIA. 相似文献
16.
Let be open, let be the Dirac operator in and let be the Clifford algebra constructed over the quadratic space . If for fixed, denotes the space of r-vectors in , then an -valued smooth function W = W
r
+ W
r+2 in Ω is said to satisfy the Moisil-Théodoresco system if . In terms of differential forms, this means that the corresponding - valued smooth form w = w
r
+ w
r+2 satisfies in Ω the system d
*
w
r
= 0, dw
r
+ d
*
w
r+2 = 0; dw
r+2 = 0.
Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure
theorem is proved for the solutions of the Moisil-Théodoresco system.
相似文献
17.
18.
Zhaoli Liu Jiabao Su Zhi-Qiang Wang 《Calculus of Variations and Partial Differential Equations》2009,35(4):463-480
In this paper, we study existence of nontrivial solutions to the elliptic equation
and to the elliptic system
where Ω is a bounded domain in with smooth boundary ∂Ω, , f (x, 0) = 0, with m ≥ 2 and . Nontrivial solutions are obtained in the case in which the nonlinearities have linear growth. That is, for some c > 0, for and , and for and , where I
m
is the m × m identity matrix. In sharp contrast to the existing results in the literature, we do not make any assumptions at infinity
on the asymptotic behaviors of the nonlinearity f and .
Z. Liu was supported by NSFC(10825106, 10831005). J. Su was supported by NSFC(10831005), NSFB(1082004), BJJW-Project(KZ200810028013)
and the Doctoral Programme Foundation of NEM of China (20070028004). 相似文献
19.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,157(1):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have . Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have . We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d.
B. Burgstaller was supported by the Austrian Schr?dinger stipend J2471-N12. 相似文献
20.
The main result of this work is a Dancer-type bifurcation result for the quasilinear elliptic problem
Here, Ω is a bounded domain in denotes the Dirichlet p-Laplacian on , and is a spectral parameter. Let μ1 denote the first (smallest) eigenvalue of −Δ
p
. Under some natural hypotheses on the perturbation function , we show that the trivial solution is a bifurcation point for problem (P) and, moreover, there are two distinct continua, and , consisting of nontrivial solutions to problem (P) which bifurcate from the set of trivial solutions at the bifurcation point (0, μ1). The continua and are either both unbounded in E, or else their intersection contains also a point other than (0, μ1). For the semilinear problem (P) (i.e., for p = 2) this is a classical result due to E. N. Dancer from 1974. We also provide an example of how the union looks like (for p > 2) in an interesting particular case.
Our proofs are based on very precise, local asymptotic analysis for λ near μ1 (for any 1 < p < ∞) which is combined with standard topological degree arguments from global bifurcation theory used in Dancer’s original
work.
Submitted: July 28, 2007. Accepted: November 8, 2007. 相似文献
((P)) |