共查询到20条相似文献，搜索用时 31 毫秒
1.
L. Olsen 《Monatshefte für Mathematik》2005,146(2):143-157
For a probability measure μ on a subset of
, the lower and upper Lq-dimensions of order
are defined by
We study the typical behaviour (in the sense of Baire’s category) of the Lq-dimensions
and
. We prove that a typical measure μ is as irregular as possible: for all q ≥ 1, the lower Lq-dimension
attains the smallest possible value and the upper Lq-dimension
attains the largest possible value. 相似文献
2.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp（0〈p〈1）Spaces 总被引：1，自引：0，他引：1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
3.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
4.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
where φ
r
is the perfect Euler spline, on the segment [a, b] of monotonicity of x for q ≥ 1 and for arbitrary q > 0 in the case where r = 2 or r = 3.
As a corollary, we prove the well-known Ligun inequality for periodic functions x ∈ L
∞
r
, namely,
for q ∈ [0, 1) in the case where r = 2 or r = 3.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1338–1349, October, 2008. 相似文献
5.
Patrick Winkert 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):289-302
In this paper we prove the L
∞-boundedness of solutions of the quasilinear elliptic equation
|
$ {ll}
Au \, = f(x,u,\nabla u) &\quad \rm{in }\, \Omega, \\
\dfrac{\partial u}{ \partial \nu} \, = g(x,u) &\quad \rm{on }\, \partial \Omega,
$ \begin{array}{ll}
Au \, = f(x,u,\nabla u) &\quad \rm{in }\, \Omega, \\
\dfrac{\partial u}{ \partial \nu} \, = g(x,u) &\quad \rm{on }\, \partial \Omega,
\end{array} 相似文献
6.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
7.
We study the vector p-Laplacian
8.
YunYanYANG 《数学学报(英文版)》2003,19(1):63-68
In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions. 相似文献
9.
We prove the following statement.
Let , and let . Suppose that, for all and , the sequence satisfies the relation
10.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引：7，自引：0，他引：7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
11.
Milutin Dostanić 《Journal d'Analyse Mathématique》2008,104(1):13-23
It is shown that the Berezin transform B on L
p
(D), where D is the unit disc, has norm
. Furthermore, the norms of a family of operators (on L
p
(D)) whose kernels are moduli of Bergman type kernels are also calculated.
Partially supported by MNZZS, Grant
ON144010 相似文献
12.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
13.
Aleksander Ćwiszewski 《Journal of Evolution Equations》2007,7(1):1-33
In the paper a topological degree is constructed for the class of maps of the form − A + F where M is a closed neighborhood retract in a Banach space
is a m-accretive map such that − A generates a compact semigroup and F : M→ E is a locally Lipschitz map. The obtained degree is applied to studying the existence and branching of periodic points of
differential inclusions of the type
14.
Jacques Giacomoni Sweta Tiwari Guillaume Warnault 《NoDEA : Nonlinear Differential Equations and Applications》2016,23(3):24
We discuss the existence and uniqueness of the weak solution of the following quasilinear parabolic equation 相似文献
$$\left\{\begin{array}{ll}u_t-\Delta _{p(x)}u = f(x,u)&\quad \text{in }\quad Q_T \stackrel{{\rm{def}}}{=} (0,T)\times\Omega,\\u = 0 & \quad\text{on}\quad \Sigma_T\stackrel{{\rm{def}}}{=} (0,T)\times\partial\Omega,\\u(0,x)=u_0(x)& \quad \text{in}\quad \Omega \end{array}\right.\quad\quad (P_{T})$$ 15.
Noriko Mizoguchi 《Mathematische Annalen》2007,339(4):839-877
A solution u of a Cauchy problem for a semilinear heat equation
16.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
17.
Octavian G. Mustafa 《Annali di Matematica Pura ed Applicata》2008,187(2):187-196
Via an integral transformation, we establish two embedding results between the Emden-Fowler type equation , t ≥ t
0 > 0, with solutions x such that as , , and the equation , u > 0, with solutions y such that for given k > 0. The conclusions of our investigation are used to derive conditions for the existence of radial solutions to the elliptic
equation , , that blow up as in the two dimensional case.
相似文献
18.
The purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: for any nonnegative integral weight function w defined on E(M),
19.
Abstract
The singular second-order m-point boundary value problem
20.
Djairo G. de Figueiredo João Marcos do Ó Bernhard Ruf 《Journal of Fixed Point Theory and Applications》2008,4(1):77-96
We establish a priori bounds for positive solutions of semilinear elliptic systems of the form
|