共查询到20条相似文献,搜索用时 31 毫秒
1.
Here we study the local or global behaviour of the solutions of elliptic inequalities involving quasilinear operators of the
type
or
. We give integral estimates and nonexistence results. They depend on properties of the supersolutions of the equationsL
A
u=0,L
B
v=0, which suppose weak coercivity conditions. Under stronger conditions, we give pointwise estimates in case of equalities,
using Harnack properties. 相似文献
2.
Pascale Vitse 《Archiv der Mathematik》2005,85(4):374-385
For Banach space operators T satisfying the Tadmor-Ritt condition
a band limited H∞ calculus is established,
where
and a is at most of the order C(T)5. It follows that such a T allows a bounded Besov algebra B∞ 10 functional calculus,
These estimates are sharp in a convenient sense. Relevant embedding theorems for B∞ 10 are derived.
Received: 25 October 2004; revised: 31 January 2005 相似文献
3.
Hoai-Minh Nguyen 《Journal d'Analyse Mathématique》2007,101(1):367-395
In this paper, we prove the estimate
, for every δ ∈ (0, ℓN), where C = C(N) is a positive constant depending only on N and
. We show that the constant ℓN in this estimate is optimal. We also present a class of maps from
into
, strictly larger than
, on which we can define the notion of degree and for which the previous inequality still holds. 相似文献
4.
We consider two-phase metrics of the form ϕ(x, ξ) ≔
, where α,β are fixed positive constants and B
α, B
β are disjoint Borel sets whose union is ℝN, and prove that they are dense in the class of symmetric Finsler metrics ϕ satisfying
. Then we study the closure
of the class
of two-phase periodic metrics with prescribed volume fraction θ of the phase α. We give upper and lower bounds for the class
and localize the problem, generalizing the bounds to the non-periodic setting. Finally, we apply our results to study the
closure, in terms of Γ-convergence, of two-phase gradient-constraints in composites of the type f(x, ∇ u) ≤ C(x), with C(x) ∈ {α, β } for almost every x. 相似文献
5.
De-xiang Ma Wei-gao Ge Xue-gang Chen 《应用数学学报(英文版)》2005,21(4):661-670
In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{( φp(u'))'+q(t)f(t,u,u')=0,0〈t〈1,u(0)=∑i=1^nαiu(ξi),u'(1)=∑i=1^nβiu'(ξi),whereφp(s)=|s|^p-2s,p≥2;ξi∈(0,1)(i=1,2,…,n),0≤αi,βi〈1(i=1,2,…n),0≤∑i=1^nαi,∑i=1^nβi〈1,and q(t) may be singular at t=0,1,f(t,u,u')may be singular at u'=0 相似文献
6.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
7.
Jacob Korevaar 《Journal d'Analyse Mathématique》2001,85(1):177-194
For entire functionsf whose power series have Hadamard gaps with ratio ≥1+α>1, Gaier has shown that the condition |f(x)|≤e
x forx≥0 implies |f(z)|≤C
αe|z| (*) for allz. Here the result is extended to the case of square root gaps, that is,
, with
, where α>0. Smaller gaps cannot work. In connection with his proof of the general high indices theorem for Borel summability,
Gaier had shown that square root gaps imply
. Having such an estimate, one can adapt Pitt’s Tauberian method for the restricted Borel high indices theorem to show that,
in fact,
, which implies (*). The author also states an equivalent distance formula involving monomialsx
pke−xinL
∞ (0, ∞). 相似文献
8.
Bao-huai Sheng 《应用数学学报(英文版)》2005,21(4):529-536
Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f(x)∈L^p(S^q-1),f(x)≥0,f absohutely unegual to 0,1≤p≤+∞,Then,it is proved in the present paper that there is a spherical harmonics PN(x) of order≤N and a constant C〉0 such that where ω(f,δ)L^p=sup 0〈t≤δ‖St(f)-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω(f,N^-1)L^p,St(f,μ)=1/|S^q-2|Sin^2λt ∫-μμ’=t f(μ')dμ' is a translation operator. 相似文献
9.
Let
be a polynomial degreen and let
. Then according to Bernstein’s inequality ‖p’‖≤n‖p‖. It is a well known open problem to obtain inequality analogous to Bernstein’s
inequality for the class IIn of polynomials satisfying p(z)≡znp(1/z). Here we obtain an inequality analogous to Bernstein’s inequality for a subclass of IIn. Our results include several of the known results as special cases. 相似文献
10.
K. F. Cheng 《Annals of the Institute of Statistical Mathematics》1982,34(1):479-489
Summary Letf
n
(p)
be a recursive kernel estimate off
(p) thepth order derivative of the probability density functionf, based on a random sample of sizen. In this paper, we provide bounds for the moments of
and show that the rate of almost sure convergence of
to zero isO(n
−α), α<(r−p)/(2r+1), iff
(r),r>p≧0, is a continuousL
2(−∞, ∞) function. Similar rate-factor is also obtained for the almost sure convergence of
to zero under different conditions onf.
This work was supported in part by the Research Foundation of SUNY. 相似文献
11.
César E. Torres Ledesma Nemat Nyamoradi 《Journal of Applied Mathematics and Computing》2017,55(1-2):257-278
In the present paper, we deal with the existence and multiplicity of solutions for the following impulsive fractional boundary value problem where \(\alpha \in (1/p, 1]\), \(1<p<\infty \), \(0 = t_0<t_1< t_2< \cdots< t_n < t_{n+1} = T\), \(f:[0,T]\times \mathbb {R} \rightarrow \mathbb {R}\) and \(I_j : \mathbb {R} \rightarrow \mathbb {R}\), \(j = 1, \ldots , n\), are continuous functions, \(a\in C[0,T]\) and By using variational methods and critical point theory, we give some criteria to guarantee that the above-mentioned impulsive problems have at least one weak solution and a sequences of weak solutions.
相似文献
$$\begin{aligned} {_{t}}D_{T}^{\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t)\right) + a(t)|u(t)|^{p-2}u(t)= & {} f(t,u(t)),\;\;t\ne t_j,\;\;\hbox {a.e.}\;\;t\in [0,T],\\ \Delta \left( {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t_j)\right) \right)= & {} I_j(u(t_j))\;\;j=1,2,\ldots ,n,\\ u(0)= & {} u(T) = 0. \end{aligned}$$
$$\begin{aligned} \Delta \left( {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t_j)\right) \right)= & {} {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right| ^{p-2}{_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right) \\&- {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j^-)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u\left( t_j^-\right) \right) ,\\ {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right| ^{p-2}{_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right)= & {} \lim _{t \rightarrow t_j^+} {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t)\right) ,\\ {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j^-)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t_j^-)\right)= & {} \lim _{t\rightarrow t_j^-}{_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t)\right) . \end{aligned}$$
12.
V. V. Andrievskii 《Journal d'Analyse Mathématique》2005,96(1):283-295
LetG⊂C be a quasidisk,K ⊂ G be a compact set, andp
n be a non-constant complex polynomial of degree at mostn. We establish the inequality
whereα
n < 0 depends onn, K,
and the geometrical structure of ϖG. 相似文献
13.
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
14.
Rajendra Bhatia 《印度理论与应用数学杂志》2010,41(1):99-111
Lipschitz continuity of the matrix absolute value |A| = (A*A)1/2 is studied. Let A and B be invertible, and let M
1 = max(‖A‖, ‖B‖), M
2 = max(‖A
−1‖, ‖B
−1‖). Then it is shown that
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
相似文献
15.
H. G. Ghazaryan V. N. Margaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(4):239-249
It is proved that if P(D) is a regular, almost hypoelliptic operator and
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