共查询到20条相似文献,搜索用时 31 毫秒
1.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献
2.
For the cyclotomic
\mathbb Z2{\mathbb Z_2}-extension k
∞ of an imaginary quadratic field k, we consider whether the Galois group G(k
∞) of the maximal unramified pro-2-extension over k
∞ is abelian or not. The group G(k
∞) is abelian if and only if the nth layer of the
\mathbb Z2{\mathbb {Z}_2}-extension has abelian 2-class field tower for all n ≥ 1. The purpose of this paper is to classify all such imaginary quadratic fields k in part by using Iwasawa polynomials. 相似文献
3.
The existence of positive radial solutions of the equation -din( |Du|p-2Du)=f(u) is studied in annular domains in Rn,n≥2. It is proved that if f(0)≥0, f is somewherenegative in (0,∞), limu→0^ f‘ (u)=0 and limu→∞ (f(u)/u^p-1)=∞, then there is alarge positive radial solution on all annuli. If f(0)≤0 and satisfies certain conditions, then the equation has no radial solution if the annuli are too wide. 相似文献
4.
Walter Senn 《manuscripta mathematica》1991,71(1):45-65
We consider a variational problem with an integrandF:R
n
×R×R
n
→R that isZ-periodic in the firstn+1 variables and satisfies certain growth-conditions. By a recent result of Moser, there exist for every α∈R
n
minimal solutionsu:R
n
→R minimising ƒF(x, u(x), u
x
(x)) dx with respect to compactly supported variations ofu and such that sup |u(x)-αx|<∞. Given such a minimal solutionu we define the average action
(whereB
r
is ther-ball around 0∈R
n
) and show thatM(α) is indeed independent of the minimal solutionu satisfying sup |u(x)-αx|<∞. We prove that this average actionM(α) is strictly convex in α.
相似文献
5.
A construction is given which, for any zonoidZ⊂R
d
and any unit vectorsu
1,...,u
k
, produces a zonotopeZ′ which is a sum of at mostk segments and has the same support values asZ in the directionsu
1
,..., u
k
. Applications to an estimation problem for fiber processes are also given as well as some related results for convex bodies. 相似文献
6.
H. E. A. Campbell I. Hughes F. Pappalardi P. S. Selick 《Commentarii Mathematici Helvetici》1991,66(1):322-331
In [1] the first and last authors studied a decomposition ofH
*(R
P
∞×…×R
P
∞;F
2) into modules over the Steenrod algebra obtained from an action of the cyclic group
. Here a minimal set of generators for the ring of invariants is characterized and counted by analyzing the associated ring
of Laurent polynomials. A structure theorem for the ring of invariant Laurent polynomials is given and a ‘destabilisation
cancels localisation’ theorem is obtained.
The authors gratefully acknowledge the support of NSERC. 1980 Mathematics Subject classification, 13F20, 55. Keywords: Invariant
theory, Steenrod algebra. 相似文献
7.
Giuseppina Vannella 《Annali di Matematica Pura ed Applicata》2002,180(4):429-440
We consider a Neumann problem of the type -εΔu+F
′(u(x))=0 in an open bounded subset Ω of R
n
, where F is a real function which has exactly k maximum points.
Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.
Received: October 30, 1999 Published online: December 19, 2001 相似文献
8.
In this article we study the exponential behavior of the continuous stochastic Anderson model, i.e. the solution of the stochastic
partial differential equation u(t,x)=1+∫0tκΔxu (s,x) ds+∫0t W(ds,x) u (s,x), when the spatial parameter x is continuous, specifically x∈R, and W is a Gaussian field on R+×R that is Brownian in time, but whose spatial distribution is widely unrestricted. We give a partial existence result of the
Lyapunov exponent defined as limt→∞t−1 log u(t,x). Furthermore, we find upper and lower bounds for lim supt→∞t−1 log u(t,x) and lim inft→∞t−1 log u(t,x) respectively, as functions of the diffusion constant κ which depend on the regularity of W in x. Our bounds are sharper, work for a wider range of regularity scales, and are significantly easier to prove than all previously
known results. When the uniform modulus of continuity of the process W is in the logarithmic scale, our bounds are optimal.
This author's research partially supported by NSF grant no. : 0204999 相似文献
9.
Kazuhiro Takimoto 《Calculus of Variations and Partial Differential Equations》2006,26(3):357-377
We consider the boundary blowup problem for k-curvature equation, i.e., H
k
[u] = f(u) g(|Du|) in an n-dimensional domain Ω, with the boundary condition u(x) → ∞ as dist (x,∂Ω) → 0. We prove the existence result under some hypotheses. We also establish the asymptotic behavior of a solution near the boundary ∂Ω.
Mathematics Subject Classification (2000) 35J65, 35B40, 53C21 相似文献
10.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
11.
Let {ξ(t), t ∈ T} be a differentiable (in the mean-square sense) Gaussian random field with E
ξ(t) ≡ 0, D
ξ(t) ≡ 1, and continuous trajectories defined on the m-dimensional interval
T ì \mathbbRm T \subset {\mathbb{R}^m} . The paper is devoted to the problem of large excursions of the random field ξ. In particular, the asymptotic properties of the probability P = P{−v(t) < ξ(t) < u(t), t ∈ T}, when, for all t ∈ T, u(t), v(t) ⩾ χ, χ → ∞, are investigated. The work is a continuation of Rudzkis research started in [R. Rudzkis, Probabilities of large excursions
of empirical processes and fields, Sov. Math., Dokl., 45(1):226–228, 1992]. It is shown that if the random field ξ satisfies certain smoothness and regularity conditions, then P = e−Q
+ Qo(1), where Q is a certain constructive functional depending on u, v, T, and the matrix function R(t) = cov(ξ′(t), ξ′(t)). 相似文献
12.
Consider the retarded difference equationx
n
−x
n−1
=F(−f(x
n
)+g(x
n−k
)), wherek is a positive integer,F,f,g:R→R are continuous,F andf are increasing onR, anduF(u)>0 for allu≠0. We show that whenf(y)≥g(y) (resp. f(y)≤g(y)) fory∈R, every solution of (*) tends to either a constant or −∞ (resp. ∞) asn→∞. Furthermore, iff(y)≡g(y) fory∈R, then every solution of (*) tends to a constant asn→∞.
Project supported by NNSF (19601016) of China and NSF (97-37-42) of Hunan 相似文献
13.
Given a semi-convex functionu: ω⊂R
n→R and an integerk≡[0,1,n], we show that the set ∑k defined by
相似文献
14.
Guido Cortesani 《Annali dell'Universita di Ferrara》1997,43(1):27-49
Let Ω be an open and bounded subset ofR
n
with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R
m
) whose jump setS
vis essentially closed and polyhedral and which are of classW
k, ∞ (S
v,R
m) for every integerk are strongly dense inGSBV
p(Ω,R
m
), in the sense that every functionu inGSBV
p(Ω,R
m
) is approximated inL
p(Ω,R
m
) by a sequence of functions {v
k{j∈N with the described regularity such that the approximate gradients ∇v
jconverge inL
p(Ω,R
nm
) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS
v
j converges to the (n−1)-dimensional measure ofS
u. The structure ofS
v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneu∈GSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.相似文献 15.
Martin Kružík 《Applications of Mathematics》2007,52(6):529-543
We study convergence properties of {υ(∇u
k
)}k∈ℕ if υ ∈ C(ℝ
m×m
), |υ(s)| ⩽ C(1+|s|
p
), 1 < p < + ∞, has a finite quasiconvex envelope, u
k
→ u weakly in W
1,p
(Ω; ℝ
m
) and for some g ∈ C(Ω) it holds that ∫Ω
g(x)υ(∇u
k
(x))dx → ∫Ω
g(x)Qυ(∇u(x))dx as k → ∞. In particular, we give necessary and sufficient conditions for L
1-weak convergence of {det ∇u
k
}
k∈ℕ to det ∇u if m = n = p.
Dedicated to Jiří V. Outrata on the occasion of his 60th birthday
This work was supported by the grants IAA 1075402 (GA AV ČR) and VZ6840770021 (MŠMT ČR). 相似文献
16.
Antonio Leaci 《manuscripta mathematica》1992,75(1):429-441
We prove the existence of a minimizing pair for the functionalG defined for every closed setK ⊂R
2 and for every functionu ∈C
1(ω/K) by
where ω is an open set inR
2, λ, μ>0,q≥1,g ∈L
q
(ω) ∩L
p
(ω) withp>2q andH
1 is the 1-dimensional Hausdorff measure. 相似文献
17.
18.
Analysis of a Free Boundary Problem Modeling Tumor Growth 总被引:4,自引:0,他引:4
Shang Bin CUI 《数学学报(英文版)》2005,21(5):1071-1082
In this paper, we study a free boundary problem arising from the modeling of tumor growth. The problem comprises two unknown functions: R = R(t), the radius of the tumor, and u = u(r, t), the concentration of nutrient in the tumor. The function u satisfies a nonlinear reaction diffusion equation in the region 0 〈 r 〈 R(t), t 〉 0, and the function R satisfies a nonlinear integrodifferential equation containing u. Under some general conditions, we establish global existence of transient solutions, unique existence of a stationary solution, and convergence of transient solutions toward the stationary solution as t →∞. 相似文献
19.
Summary. A sequence of heads and tails is produced by repeatedly selecting a coin from two possible coins, and tossing it. The second
coin is tossed at renewal times in a renewal process, and the first coin is tossed at all other times. The first coin is fair (Prob(heads)=1/2), and the second coin is known either to be fair, or to have known biasθ∈(0,1] (Prob(heads) ). Letting u
k
:= Prob (There is a renewal at time k), we show that if ∑
k
=0
∞
u
k
2=∞, we can determine, using only the sequence of heads and tails produced, if the second coin had bias θ or 0. If , we show that this is not possible.
Received: 20 November 1996 / In revised form: 20 February 1997 相似文献
20.
The integrability of an m-component system of hydrodynamic type, u
t = V(u)u
x
, by the generalized hodograph method requires the diagonalizability of the m × m matrix V(u). This condition is known to be equivalent to the vanishing of the corresponding Haantjes tensor. We generalize this approach
to hydrodynamic chains—infinite-component systems of hydrodynamic type for which the ∞ × ∞ matrix V(u) is ‘sufficiently sparse’. For such systems the Haantjes tensor is well-defined, and the calculation of its components involves
finite summations only. We illustrate our approach by classifying broad classes of conservative and Hamiltonian hydrodynamic
chains with the zero Haantjes tensor. We prove that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic
chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition
for the integrability. 相似文献
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