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1.
Let $\Omega$ be a bounded Lipschitz domain in $\BBbR^n$. The Cauchy-Green, or
metric, tensor field associated with a deformation of the set $\Omega$, i.e., a smooth-enough
orientation-preserving mapping $\bTh\colon\Omega\to\BBbR^n$, is the $n\times n$ symmetric matrix field
defined by $\bnabla\bTheta^T(x)\bnabla\bTheta(x)$ at each point $x\in\Omega$. We show that, under
appropriate assumptions, the deformations depend continuously on their Cauchy-Green
tensors, the topologies being those of the spaces $\bH^1(\Omega)$ for the deformations and
$\bL^1(\Omega)$ for the Cauchy-Green tensors. When $n=3$ and $\Omega$ is viewed as a reference
configuration of an elastic body, this result has potential applications to nonlinear
three-dimensional elasticity, since the stored energy function of a hyperelastic material
depends on the deformation gradient field $\bnabla\bTheta$ through the Cauchy-Green tensor. 相似文献
2.
We obtain the necessary and sufficient conditions for the boundedness of a generalized Strichartz potential. 相似文献
3.
In this paper we study properties of linear Weingarten immersions and graphs related to non-existence problems and behaviour
of its curvatures. The main results are obtained giving a harmonic representation of linear Weingarten surfaces and by proving
optimal estimates of the height and curvatures that the immersion must satisfy, characterizing the spherical caps as the only
ones achieving these bounds.
Received January 25, 2001; in revised form April 4, 2002 相似文献
4.
WANG Silei Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2005,48(4):448-455
An all-round answer is given to the following question: "Find a necessary and sufficient size condition for an integrable compactly supported function on Rn with mean value zero to be in the Hardy space H1." Stefanov answers it only for n = 1. Equivalent answer is also given for n = 1. 相似文献
5.
We obtain estimates for the restriction of the Fourier transform to a certain k-dimensional quadratic submanifold of n.Mathematics Subject Classification (2000): 42B10Research supported in part by the grant KRF-2002-070-C 00005 of the Korea research Foundation. 相似文献
6.
Operators related to truncated Hilbert transforms on <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript> 下载免费PDF全文
Hong Hai Liu 《数学学报(英文版)》2017,33(7):1011-1020
In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H 1 to L 1, and prove variation, oscillation and λ-jump operators related to smooth truncations are bounded from H 1 to L 1. 相似文献
7.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
8.
T.A. Suslina 《Functional Analysis and Its Applications》2010,44(4):318-322
Homogenization in the small period limit for the solution ue of the Cauchy problem for a parabolic equation in Rd is studied. The coefficients are assumed to be periodic in Rd with respect to the lattice ɛG. As ɛ → 0, the solution u ɛ converges in L2(Rd) to the solution u0 of the effective problem with constant coefficients. The solution u ɛis approximated in the norm of the
Sobolev space H
1(Rd) with error O( ɛ); this approximation is uniform with respect to the L2-norm of the initial data and contains a corrector
term of order ɛ. The dependence of the constant in the error estimate on time t is given. Also, an approximation in H
1(Rd) for the solution of the Cauchy problem for a nonhomogeneous parabolic equation is obtained. 相似文献
9.
Zhang Pu Wu Huoxiong 《高校应用数学学报(英文版)》2005,20(4):455-461
Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO(R^n). It is proved that μΩ,bis bounded from the Hardy space H^1 (R^n) into the weak L^1(R^n) space. 相似文献
10.
A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection. 相似文献
11.
The negative ion yields φ (H?) and the neutral atom yields φ (H) of 0.6, 0.9, 1.2, 1.6 and 1.8 MeV H+ projectiles traversing various carbon foils have been measured. The experimental results showed that neither φ(H?) nor φ(H) varies with the dwell time ^ at the same energy. φ(H)is larger than φ(H?) by about 3–4 orders of magnitude. The charge exchanging between H+ ions and carbon foils was analyzed. It can be seen that the charge exchange is the most basic process. The experience formula of σc/σl has been gotten. 相似文献
12.
Takeshi Kawazoe 《分析论及其应用》2009,25(3):201-229
For α≥β≥ -1/2 let Δ(x) = (2shx)2α+1(2chx)2β+1 denote the weight function on R+ and L1(Δ) the space of integrable functions on R+ with respect to Δ(x)dx, equipped with a convolution structure. For a suitable φ∈ L1(Δ), we put φt(x) = t-1Δ(x)-1Δ(x/t)φ(x/t) for t > 0 and define the radial maximal operator Mφ as usual manner. We introduce a real Hardy space H1(Δ) as the set of all locally integrable functions f on R+ whose radial maximal function Mφ(f) belongs to L1(Δ). In this paper we obtain a relation between... 相似文献
13.
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition
and may not be doubling, we define the product of functions in the regular BMO and the atomic block H
1 in the sense of distribution, and show that this product may be split into two parts, one in L
1 and the other in some Hardy-Orlicz space. 相似文献
14.
We show that if U* is a hypercover of a topological space X then the natural map hocolim U* X is a weak equivalence. This fact is used to construct topological realization functors for the 1-homotopy theory of schemes over real and complex fields. In an appendix, we also prove a theorem about computing homotopy colimits of spaces that are not cofibrant.Mathematics Subject Classification (2000):55U35, 14F20, 14F42The second author was supported by an NSF Postdoctoral Research Fellowship 相似文献
15.
Countably generated prime ideals in <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript>
We confirm a twenty year old conjecture by showing that a nonzero prime ideal P in the algebra H∞ of bounded analytic functions in the open unit disk is countably generated if and only if it is either a principal ideal
generated by the polynomial z−z0, |z0|<1, or if P is generated by the n-th roots of an atomic inner function. The case of the algebra H∞+C is also dealt with.
Dedicated to the 70th birthday of Joseph Cima
Research supported by the RIP-program Oberwolfach 2004. 相似文献
16.
Li Wenming 《分析论及其应用》2002,18(3):86-92
Using the maximal function characterization of Hardy spaces, we study the interpolation spaces be-tween H1 and L∞ on spaces of homogeneous type. 相似文献
17.
Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H1(Rn), we shall show the asymptotic behavior for its solutions in C(0, ∖;H1(Rn)) ∩ L2(0, ∖;H1,2n/(n-2)(R2)), n≥3. Analogous results also hold in the case that the nonlinearity has the subcritical power in H1(Rn), n≥1.
Dedicated to Professor Zhou Yulin for his 80th birthday. 相似文献
18.
Suppose $\cal{S}^1({\cal T})\subset H^1(\Omega)$ is the $P_1$-finite element
space of $\cal{T}$-piecewise affine functions
based on a regular triangulation $\cal{T}$ of a two-dimensional surface
$\Omega$ into triangles.
The $L^2$ projection $\Pi$ onto $\cal{S}^1(\cal{T})$ is $H^1$ stable
if $\norm{\Pi v}{H^1(\Omega)}\le C\norm{v}{H^1(\Omega)}$ for
all $v$ in the Sobolev space $H^1(\Omega)$ and if the bound $C$
does not depend on the mesh-size in $\cal{T}$ or on the
dimension of $\cal{S}^1(\cal{T})$.
\hskip 1em A red–green–blue refining adaptive algorithm is designed which
refines a coarse mesh $\cal{T}_0$ successively such that each triangle is
divided into one, two, three, or four subtriangles.
This is the newest vertex bisection supplemented with possible red refinements
based on a careful initialization.
The resulting finite element space allows
for an $H^1$ stable $L^2$ projection.
The stability
bound $C$ depends only on the coarse mesh $\cal{T}_0$ through the number of
unknowns, the shapes of the triangles in $\cal{T}_0$, and possible
Dirichlet boundary conditions. Our arguments also
provide a discrete version
$\norm{h_\cal{T}^{-1}\,\Pi v}{L^2(\Omega)}\le C\norm{h_\cal{T}^{-1}\,v}{L^2(\Omega)}$
in $L^2$ norms weighted with the mesh-size $h_\T$. 相似文献
19.
20.
Joseph Corneli Neil Hoffman Paul Holt George Lee Nicholas Leger Stephen Moseley Eric Schoenfeld 《Journal of Geometric Analysis》2007,17(2):189-212
We prove the double bubble conjecture in the three-sphereS
3 and hyperbolic three-spaceH
3 in the cases where we can apply Hutchings theory:
A balancing argument and asymptotic analysis reduce the problem inS
3 andH
3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces. 相似文献
– | • InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3. |
– | • inH 3, when the smaller volume is at least 85% that of the larger. |