共查询到20条相似文献,搜索用时 125 毫秒
1.
Let
\mathfrakA\mathfrak{A} be a normed algebra with identity, Ω be a locally compact Hausdorf space and λ be a positive Radon measure on Ω with supp(λ) = Ω. In this paper, we establish a necessary and sufficient condition for L
1(Ω,
\mathfrakA\mathfrak{A}) to be an algebra with pointwise multiplication. Under this condition, we then characterize compact and weakly compact left
multipliers on L
1(Ω,
\mathfrakA\mathfrak{A}). 相似文献
2.
P. Manselli 《Annali di Matematica Pura ed Applicata》2000,178(1):67-80
The subfamilyR(p, Ω) of the class of second order, uniformly elliptic, non variational operators L with bounded measurable coefficients,
such that L(W2, p (Ω)) is dense in Lp (Ω), is studied. Sufficient and necessary and sufficient conditions are given, for L to belong toR(p, Ω). An operator L of the class above and not inR(p, Ω) is constructed.
Entrata in Redazione il 5 ottobre 1998. 相似文献
3.
We consider finite element methods applied to a class of Sobolev equations inR d(d ≥ 1). Global strong superconvergence, which only requires that partitions are quais-uniform, is investigated for the error between the approximate solution and the Ritz-Sobolev projection of the exact solution. Two order superconvergence results are demonstrated inW 1,p (Ω) andL p(Ω) for 2 ≤p < ∞. 相似文献
4.
Lower semicontinuity for polyconvex functionals of the form ∫Ω
g(detDu)dx with respect to sequences of functions fromW
1,n
(Ω;ℝ
n
) which converge inL
1 (Ωℝ
n
) and are uniformly bounded inW
1,n−1 (Ω;ℝ
n
), is proved. This was first established in [5] using results from [1] on Cartesian Currents. We give a simple direct proof
which does not involve currents. We also show how the method extends to prove natural, essentially optimal, generalizations
of these results.
Supported by MURST, Gruppo Nazionale 40%
Partially supported by Australian Research Council 相似文献
5.
Guido Cortesani 《Annali dell'Universita di Ferrara》1997,43(1):27-49
Let Ω be an open and bounded subset ofR
n
with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R
m
) whose jump setS
vis essentially closed and polyhedral and which are of classW
k, ∞ (S
v,R
m) for every integerk are strongly dense inGSBV
p(Ω,R
m
), in the sense that every functionu inGSBV
p(Ω,R
m
) is approximated inL
p(Ω,R
m
) by a sequence of functions {v
k{j∈N with the described regularity such that the approximate gradients ∇v
jconverge inL
p(Ω,R
nm
) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS
v
j converges to the (n−1)-dimensional measure ofS
u. The structure ofS
v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneu∈GSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.相似文献
6.
Riccardo De Arcangelis 《Annali dell'Universita di Ferrara》1989,35(1):135-145
Summary Letf: (x, z)∈R
n×Rn→f(x, z)∈[0, +∞] be measurable inx and convex inz.
It is proved, by an example, that even iff verifies a condition as|z|
p≤f(x, z)≤Λ(a(x)+|z|q) with 1<p<q,a∈L
loc
s
(R
n),s>1, the functional
that isL
1(Ω)-lower semicontinuous onW
1,1(Ω), does not agree onW
1,1(Ω) with its relaxed functional in the topologyL
1(Ω) given by inf
Riassunto Siaf: (x, z)∈R n×Rn→f(x, z)∈[0, +∞] misurabile inx e convessa inz. Si mostra con un esempio che anche sef verifica una condizione del tipo|z| p≤f(x, z)≤Λ(a(x)+|z|q) con 1<p<q,a∈L loc s (R n),s>1, il funzionale , che èL 1(Ω)-semicontinuo inferiormente suW 1,1(Ω), non coincide suW 1,1(Ω) con il suo funzionale rilassato nella topologiaL 1(Ω) definito da inf相似文献
7.
Martin Kružík 《Applications of Mathematics》2007,52(6):529-543
We study convergence properties of {υ(∇u
k
)}k∈ℕ if υ ∈ C(ℝ
m×m
), |υ(s)| ⩽ C(1+|s|
p
), 1 < p < + ∞, has a finite quasiconvex envelope, u
k
→ u weakly in W
1,p
(Ω; ℝ
m
) and for some g ∈ C(Ω) it holds that ∫Ω
g(x)υ(∇u
k
(x))dx → ∫Ω
g(x)Qυ(∇u(x))dx as k → ∞. In particular, we give necessary and sufficient conditions for L
1-weak convergence of {det ∇u
k
}
k∈ℕ to det ∇u if m = n = p.
Dedicated to Jiří V. Outrata on the occasion of his 60th birthday
This work was supported by the grants IAA 1075402 (GA AV ČR) and VZ6840770021 (MŠMT ČR). 相似文献
8.
Bin Han 《Advances in Computational Mathematics》2006,24(1-4):375-403
In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space Wpk(ℝs) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented.
Rate of convergence of vector cascade algorithms in a Sobolev space Wpk(ℝs) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the Lp (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function
vector. As a consequence, we show that if a compactly supported function vector φ∈Lp(ℝs) (φ∈C(ℝs) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz
space Lip(ν,Lp(ℝs)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167)
in the univariate setting to the multivariate setting.
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C20, 41A25, 39B12.
Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant
G121210654. 相似文献
9.
This paper considers the dual of anisotropic Sobolev spaces on any stratified groups 𝔾. For 0≤k<m and every linear bounded functional T on anisotropic Sobolev space W
m−k,p
(Ω) on Ω⊂𝔾, we derive a projection operator L from W
m,p
(Ω) to the collection 𝒫
k+1
of polynomials of degree less than k+1 such that T(X
I
(Lu))=T(X
I
u) for all uW
m,p
(Ω) and multi-index I with d(I)≤k. We then prove a general Poincaré inequality involving this operator L and the linear functional T. As applications, we often choose a linear functional T such that the associated L is zero and consequently we can prove Poincaré inequalities of special interests. In particular, we obtain Poincaré inequalities
for functions vanishing on tiny sets of positive Bessel capacity on stratified groups. Finally, we derive a Hedberg-Wolff
type characterization of measures belonging to the dual of the fractional anisotropic Sobolev spaces W
α,p
𝔾.
Received: 25 March 2002; in final form: 10 September 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (1991): 46E35, 41A10, 22E25
The second author was supported partly by U.S NSF grant DMS99-70352 and the third author was supported partly by NNSF grant
of China. 相似文献
10.
We prove the uniqueness of weak solutions of the time-dependent 3-D Ginzburg-Landau model for superconductivity with (Ψ
0, A
0) ∈ L
2(Ω) initial data under the hypothesis that (Ψ, A) ∈ C([0, T]; L
3(Ω)) using the Lorentz gauge.
相似文献
11.
Harri Ojanen 《Journal of Fourier Analysis and Applications》2000,6(4):427-436
Weighted Lp estimates (1<p<∞) are shown for oscillatory singular integral operators with polynomial phase and a rough kernel of the form
eiP(x,y)Ω(x−y)h(|x−y|)|x−y|−n. We assume that Ω∈L logL(Sn−1) is homogeneous of degree zero and ∫Sn-1Ω=0. The radial factor h has bounded variation. The necessary condition on the weight is similar to the Ap condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to Ω. 相似文献
12.
A. A. Kovalevskii 《Ukrainian Mathematical Journal》1996,48(9):1402-1422
By using special local characteristics of domains Ω
s
⊂Ω,s=12,..., we establish necessary and sufficient conditions for the γ-convergence of sequences of integral functionalsI
λs
:W
k,m
(Ω
s
)→ℝ, λ⊂Ω to interal functionals defined on W
k,m
(Ω).
Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk. Translated from Ukrainskii Matematicheskii
Zhurnal, Vol. 48, No. 9, pp. 1236–1254, September, 1996. 相似文献
13.
This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results
on equidistant systems of points in a Hilbert space to the case of the space L
2(Ω, F, ℙ) of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular
sequence of random variables (elements of which are taken from sets of equidistant elements of L
2(Ω, F, ℙ) to be orthogonal to some other sequence in L
2(Ω, F, ℙ). The result obtained is interesting from the point of view of the time series analysis, since it can be applied to a
class of sequences random variables that exhibit a monotonically increasing variance. An application to ergodic theorem is
also provided. 相似文献
14.
Aissa Guesmia 《Israel Journal of Mathematics》2001,125(1):83-92
We consider in this paper the evolution systemy″−Ay=0, whereA =∂
i(aij∂j) anda
ij ∈C
1 (ℝ+;W
1,∞ (Ω)) ∩W
1,∞ (Ω × ℝ+), with initial data given by (y
0,y
1) ∈L
2(Ω) ×H
−1 (Ω) and the nonhomogeneous conditiony=v on Γ ×]0,T[. Exact controllability means that there exist a timeT>0 and a controlv such thaty(T, v)=y′(T, v)=0. The main result of this paper is to prove that the above system is exactly controllable whenT is “sufficiently large”. Moreover, we obtain sharper estimates onT. 相似文献
15.
W. M. Zaja̧czkowski 《Journal of Mathematical Sciences》2011,178(3):265-273
The axially symmetric solutions to the Navier–Stokes equations are studied. Assume that either the radial component (v
r
) of the velocity belongs to L
∞(0, T;L
3(Ω0)) or v
r
/r belongs to L
∞(0, T;L
3/2(Ω0)), where Ω0 is a neighborhood of the axis of symmetry. Assume additionally that there exist subdomains Ω
k
, k = 1, . . . , N, such that W0 ì èk = 1N Wk {\Omega_0} \subset \bigcup\limits_{k = 1}^N {{\Omega_k}} , and assume that there exist constants α
1, α
2 such that either
|| vr ||L¥ ( 0,T;L3( Wk ) ) £ a1 or || \fracvrr ||L¥ ( 0,T;L3/2( Wk ) ) £ a2 {\left\| {{v_r}} \right\|_{{L_\infty }\left( {0,T;{L_3}\left( {{\Omega_k}} \right)} \right)}} \leq {\alpha_1}\,or\;{\left\| {\frac{{{v_r}}}{r}} \right\|_{{L_\infty }\left( {0,T;{L_{3/2}}\left( {{\Omega_k}} \right)} \right)}} \leq {\alpha_2} for k = 1, . . . , N. Then the weak solution becomes strong ( v ? W22,1( W×( 0,T ) ),?p ? L2( W×( 0,T ) ) ) \left( {v \in W_2^{2,1}\left( {\Omega \times \left( {0,T} \right)} \right),\nabla p \in {L_2}\left( {\Omega \times \left( {0,T} \right)} \right)} \right) . Bibliography: 28 titles. 相似文献
16.
GuoEnHU BoLinMA 《数学学报(英文版)》2004,20(5):785-792
The commutators of singular integral operators with homogeneous kernel Ω(x)/|x|^n are studied, where Ω is homogeneous of degree zero, and has mean value zero on the unit sphere. It is proved that Ω∈ L(logL)^(k 1)(S^(n-1)) is a sufficient condition such that the k-th order commutator is bounded on L^2(R^n). 相似文献
17.
Andreas Wannebo 《Arkiv f?r Matematik》1994,32(1):245-254
A new proof is given for a theorem by V. G. Maz'ya. It gives a necessary and sufficient condition on the open set Ω inR
N
for the functions inW
0
m,p
(Ω) to have the ordinary norm equivalent to the norm obtained when including only the highest order derivatives in the definition.
The proof is based on a kind of polynomial capacities, Maz'ya capacities. 相似文献
18.
We describe an ordinalh(A) which plays a key role in the model theory of the admissible fragmentL
A
. In particular, the Hanf number ofL
A
is ℶh(A) IfL
A
isL
κ=ω wherecf(k)>ω thenh(A) can be characterized as the least ordinal which is notH(k
+)-recursive.
Financial support received from NSF Grant GP-23114
Financial support received from NSF Grant GP-23114 and the A. P. Sloan Foundation 相似文献
19.
Jie-Cheng Chen 《Israel Journal of Mathematics》1993,81(1-2):193-202
In this paper, we get a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n, v(x)dx) to weak-L
Φ(R
+
n+1
,dμ), where Φ is anN-function satisfying the Δ2-condition. We also find a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n,v(x)dx) toL
Φ(R
+
n+1
,dμ) under some additional condition.
Partially supported by NNSF of P.R. China 相似文献
20.
Ferenc Móricz 《Journal d'Analyse Mathématique》1994,62(1):115-130
We prove the convergence inL
1([−gp, π)2)-norm of the double Fourier series of an integrable functionf(x, y) which is periodic and even with respect tox andy, with coefficientsa
jk
satisfying certain conditions of Hardy-Karamata kind, and such thata
jk
logj logk→0 asj, k→∞. These sufficient conditions become quite natural in particular cases. Then we extend these results to the convergence
of double Walsh-Fourier series inL
1 (0, 1)2)- norm. As a by-product, we obtain Tauberian conditions ensuring the convergence of a double numerical series provided it
is Cesàro summable.
This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant # 234. 相似文献