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131.
132.
Models with varying cosmic parameters, which were earlier regarded constant, are getting attention. However, different models are usually invoked to explain the evolution of different parameters. We argue that whatever physical process is responsible for the evolution of one parameter, should also be responsible for the evolution of others. This means that the different parameters are coupled together somehow. Based on this guiding principle, we investigate a Bianchi type I model with variable Λ and G, in which Λ, G and the shear parameter σ2, all are coupled. It is interesting that the resulting model reduces to the FLRW model for large t with G approaching a constant. 相似文献
133.
Vincent Mathew 《International Journal of Infrared and Millimeter Waves》2005,26(4):563-573
This paper presents an analysis of frequency dependent propagation characteristics of microstrip lines with anisotropic substrate and overlay. The method involves setting up of the Greens functions corresponding to the structure and formulating a dispersion relation in Fourier transform domain. The dispersion relation is constructed in a Galerkins procedure. Numerical results are also presented. 相似文献
134.
Let e(x, y, ) be the spectral function and the unit spectral projection operator, with respect to the Laplace–Beltrami operator on a closed Riemannian manifold M. We generalize the one-term asymptotic expansion of e(x, x, ) by Hörmander (Acta Math.
88 (1968), 341–370) to that of
x
y
e(x,y,)|
x=y
for any multiindices , in a sufficiently small geodesic normal coordinate chart of M. Moreover, we extend the sharp (L
2,L
p) (2 p) estimates of by Sogge (J. Funct. Anal.
77 (1988), 123–134; London Math. Soc. Lecture Note Ser. 137, Cambridge University Press, Cambridge, 1989; Vol. 1, pp. 416–422) to the sharp (L
2, Sobolev L
p) estimates of . 相似文献
135.
Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes 总被引:68,自引:0,他引:68
In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition K/hK c0 > 0 is not satisfied, wherehK is the diameter of the element K and K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L2-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek. 相似文献
136.
Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems 总被引:1,自引:0,他引:1
Evgenia H. Papageorgiou Nikolaos S. Papageorgiou 《Czechoslovak Mathematical Journal》2004,54(2):347-371
In this paper we examine nonlinear periodic systems driven by the vectorial p-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the sublinear problem. For the semilinear problem (i.e. p = 2) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the superlinear problem. Our work generalizes some recent results of Tang (PAMS 126(1998)). 相似文献
137.
WeiJieFENG 《数学学报(英文版)》2004,20(6):983-988
In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang‘s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems. 相似文献
138.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
139.
This paper deals with the following class of singular biharmonic problems
140.
We derive Sobolev inequalities for Besov spaces B
p,p
(F), 0<<1, 1p< on d-sets F in R
n
, dn, from a metric property of the Bessel capacity on R
n
. We first extend Kaimanovitch's result on the equivalence of Sobolev and capacitary inequalites for contractive p-norms in a general setting allowing unbounded Lévy kernels. A simple part of the Jonsson–Wallin trace theorem for Besov spaces and some basic properties of Bessel and Besov capacities on R
n
are then utilized in getting the desired inequalities. When p=2, the Besov space being considered is a non-local regular Dirichlet space and gives rise to a jump type symmetric Markov process M
over the d-set. The upper bound of the transition function of M
and metric properties of M
-polar sets are then exhibited. 相似文献