共查询到20条相似文献,搜索用时 46 毫秒
1.
Pavel Drábek Peter Takáč 《Calculus of Variations and Partial Differential Equations》2007,29(1):31-58
An improved Poincaré inequality and validity of the Palais-Smale condition are investigated for the energy functional on , 1 < p < ∞, where Ω is a bounded domain in , is a spectral (control) parameter, and is a given function, in Ω. Analysis is focused on the case λ = λ1, where −λ1 is the first eigenvalue of the Dirichlet p-Laplacian Δ
p
on , λ1 > 0, and on the “quadratization” of within an arbitrarily small cone in around the axis spanned by , where stands for the first eigenfunction of Δ
p
associated with −λ1. 相似文献
2.
Krešimir Burazin 《Annali dell'Universita di Ferrara》2008,54(2):229-243
The Cauchy problem for a semilinear hyperbolic system of the type
is considered, with each matrix function A
k
being diagonal, bounded and locally Lipschitz in x. Discrete models for the Boltzmann equation furnish examples of such systems. For bounded initial data, and right-hand side
that is locally Lipschitz and locally bounded in u, local existence and uniqueness results in L∞ are well known, together with some estimates on weak solutions. More precise estimates for weak solutions of the above Cauchy
problem will be given, supplemented by estimates on the maximal time of existence for the solution, as well as the local existence
and uniqueness in L
p
setting (1 < p < ∞).
This work is supported in part by the Croatian MZOS through project 037-0372787-2795. 相似文献
3.
Abstract The authors characterize the finite groups in which
, the intersection of the maximal non-nilpotent subgroups of G, is nilpotent, but different from Φ(G). Further, if
is a saturated formation and if
is the intersection of all maximal subgroups of G not belonging to
, a necessary and sufficient condition is given for
to be nilpotent different from Φ(G).
Keywords: Frattini subgroup, Maximal subgroups, Saturated formation
Mathematics Subject Classification (2000): 20B05, 20D10, 20D25,20E28 相似文献
4.
We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary, λ is a positive real number, and the continuous functions p
1, p
2, and q satisfy 1 < p
2(x) < q(x) < p
1(x) < N and for any . The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that any is an eigenvalue, while any is not an eigenvalue of the above problem. 相似文献
5.
Tatsuo Nishitani 《Annali dell'Universita di Ferrara》2006,52(2):395-430
Abstract The well posedness of the Cauchy problem for the operator P=Dt2–Dxa(t,x)nDx,
with data on t=0 is studied assuming a ∈ CN(
(R)), s0>1 and sufficiently close to 1, a(t,x)≥ 0. Well posedness is proved in Gevrey classes γ(s), for
, n≥ n0.
Keywords: Partial differential equations, Cauchy problem, Well posedness 相似文献
6.
Ettore Carletti 《Annali dell'Universita di Ferrara》1983,29(1):37-44
Riassunto Scopo di questo lavoro è dare una formula asintotica per il numero degli zeri di ReF
K(λ+it) e di ImF
K(λ+it), dove
eζ
K(8) è la funzione zeta di Dedekind associata al campo numericoK, con 0<t<T e λ numero reale fissato tale che 1−1/n<λ<1 doven è il grado diK.
Summary The aim of this paper is to give an asymptotic formula for the number of zeros of ReF K(λ+it) and ImF K(λ+it), where andζ K(8) is the Dedekind zeta function for a number fieldK, with 0<t<T and λ fixed real number such that 1−1/n<λ<1, wheren is the degree ofK.相似文献
7.
Abstract We examine the cut-off resolvent Rχ(λ) = χ (–ΔD – λ2)–1χ, where ΔD is the Laplacian with Dirichlet boundary condition and
equal to 1 in a neighborhood of the obstacle K. We show that if Rχ(λ) has no poles for
, then
This estimate implies a local energy decay. We study the spectrum of the Lax-Phillips semigroup Z(t) for trapping obstacles having at least one trapped ray.
Keywords: Trapping obstacles, Resonances, Local energy decay, Cut-off resolvent 相似文献
8.
The gradient method for the symmetric positive definite linear system
is as follows
where
is the residual of the system at xk and αk is the stepsize. The stepsize
is optimal in the sense that it minimizes the modulus
, where λ1 and λn are the minimal and maximal eigenvalues of A respectively. Since λ1 and λn are unknown to users, it is usual that the gradient method with the optimal stepsize is only mentioned in theory. In this
paper, we will propose a new stepsize formula which tends to the optimal stepsize as
. At the same time, the minimal and maximal eigenvalues, λ1 and λn, of A and their corresponding eigenvectors can be obtained.
This research was initiated while the first author was visiting The Hong Kong Polytechnic University.
This author was supported by the Chinese NSF grants (No. 40233029 and 101071104) and an innovation fund of Chinese Academy
of Sciences.
This author was supported by a grant from the Research Committee of the Hong Kong Polytechnic University (A-PC36). 相似文献
(1) |
9.
Consider a smooth bounded domain , and the Navier–Stokes system in with initial value and external force f = div F, where , are so-called Serrin exponents. It is an important question what is the optimal (weakest possible) initial value condition
in order to obtain a unique strong solution in some initial interval [0, T), . Up to now several sufficient conditions on u
0 are known which need not be necessary. Our main result, see Theorem 1.1, shows that the condition , A denotes the Stokes operator, is sufficient and necessary for the existence of such a strong solution u. In particular, if , , then any weak solution u in the usual sense does not satisfy Serrin’s condition for each 0 < T ≤ ∞.
相似文献
10.
Shaowei Chen Shujie Li 《Calculus of Variations and Partial Differential Equations》2006,27(1):105-123
In this paper we study the following problem:with periodic nonlinearity g, where and λ2 is the second eigenvalue of −Δ, on H
1
0(B). We proved that the problem has infinitely many solutions under some additional conditions on g and h. The method we used is a new variational reduction method.
Mathematics Subject Classi cation (2000) 35J20, 35J70 相似文献
11.
Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case 总被引:1,自引:0,他引:1
We consider the system of Fredholm integral equations
and also the system of Volterra integral equations
where T>0 is fixed and the nonlinearities h
i
(t,u
1,u
2,…,u
n
) can be singular at t=0 and u
j
=0 where j∈{1,2,…,n}. Criteria are offered for the existence of constant-sign solutions, i.e., θ
i
u
i
(t)≥0 for t∈[0,1] and 1≤i≤n, where θ
i
∈{1,−1} is fixed. We also include examples to illustrate the usefulness of the results obtained.
相似文献
12.
In this paper, we investigate an eigenvalue problem of Dirichlet Laplacian on a bounded domain Ω in an n-dimensional Euclidean space R
n
. If λ
k+1 is the (k + 1)th eigenvalue of Dirichlet Laplacian on Ω, then, we prove that, for n ≥ 41 and
and, for any n and
with
, where j
p,k
denotes the k-th positive zero of the standard Bessel function J
p
(x) of the first kind of order p. From the asymptotic formula of Weyl and the partial solution of the conjecture of Pólya, we know that our estimates are optimal in the sense of order of k.Q.-M. Cheng was partially Supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of ScienceH. Yang was partially Supported by Chinese NSF, SF of CAS and NSF of USA 相似文献
13.
Jun Wu 《Monatshefte für Mathematik》2006,149(3):259-264
For
, let E(λ*, λ*) be the set
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
where dim denotes the Hausdorff dimension. 相似文献
14.
H. Rindler 《Monatshefte für Mathematik》2006,147(3):265-272
For
, let E(λ*, λ*) be the set
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
where dim denotes the Hausdorff dimension. 相似文献
15.
Giuseppe Maria Coclite Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Silvia Romanelli 《Semigroup Forum》2008,77(1):101-108
The solution u of the well-posed problem
depends continuously on (a
ij
,β,γ,q).
Dedicated to Karl H. Hofmann on his 75th birthday. 相似文献
16.
Abstract Consider an interstellar cloud that occupies the region
, bounded by the known surface
, and assume that the scattering cross section σs and the total cross section σ are also known. Then, we prove that it is possible to identify the source q=q(x,t) that produces UV-photons inside the cloud, provided that the UV-photon distribution function arriving at a location
, far from the cloud, is measured at times
,
, ...,
.
Keywords: Photon transport, Semigroups and linear evolution equations, Inverse problems
Mathematics Subject Classification (2000): 82A25, 82C70, 34K29, 65M32 相似文献
17.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献
18.
Liselott Flodén Anders Holmbom Marianne Olsson Nils Svanstedt 《Annali dell'Universita di Ferrara》2007,53(2):217-232
Reiterated homogenization is studied for divergence structure parabolic problems of the form . It is shown that under standard assumptions on the function a(y
1,y
2,t,ξ) the sequence of solutions converges weakly in to the solution u of the homogenized problem .
相似文献
19.
Flávio Dickstein Miguel Loayza 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(1):1-23
We consider the Cauchy problem for the weakly coupled parabolic system ∂
t
w
λ−Δ w
λ = F(w
λ) in R
N
, where λ > 0, w
λ = (u
λ, v
λ), F(w
λ) = (v
λ
p
, u
λ
q
) for some p, q ≥ 1, pq > 1, and , for some nonnegative functions φ1, φ2
C
0(R
N
). If (p, q) is sub-critical or either φ1 or φ2 has slow decay at ∞, w
λ blows up for all λ > 0. Under these conditions, we study the blowup of w
λ for λ small.
相似文献
20.
Leonid Gurvits 《Discrete and Computational Geometry》2009,41(4):533-555
Let K=(K
1,…,K
n
) be an n-tuple of convex compact subsets in the Euclidean space R
n
, and let V(⋅) be the Euclidean volume in R
n
. The Minkowski polynomial V
K
is defined as V
K
(λ
1,…,λ
n
)=V(λ
1
K
1+⋅⋅⋅+λ
n
K
n
) and the mixed volume V(K
1,…,K
n
) as
Our main result is a poly-time algorithm which approximates V(K
1,…,K
n
) with multiplicative error e
n
and with better rates if the affine dimensions of most of the sets K
i
are small. Our approach is based on a particular approximation of log (V(K
1,…,K
n
)) by a solution of some convex minimization problem. We prove the mixed volume analogues of the Van der Waerden and Schrijver–Valiant
conjectures on the permanent. These results, interesting on their own, allow us to justify the abovementioned approximation
by a convex minimization, which is solved using the ellipsoid method and a randomized poly-time time algorithm for the approximation
of the volume of a convex set. 相似文献