共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Let Ω
ϕ
r
={f:f
(r-1) abs. cont. on [0,1], ‖qr(D)f‖p≤1, f(2K+σ) (0)=f(2K+σ)=0, (k)=0,...,l-1}. where
, and I is an identical operator. Denote Kolmogorov, linear, Geelfand and Bernstein n-widths of Ω
ϕ
r
in Lp byd
n
(Ω
ϕ
r
;L
p
),δ
n
(Ω
ϕ
r
;L
p
),d
n
(Ω
p
r
;L
p
) andb
n
(Ω
p
r
;L
p
), respectively. In this paper, we find a method to get an exact estimation of these n-widths. Related optimal subspaces and
an optimal linear operator are given. For another subset
, similar results are also derrived. 相似文献
3.
Jack D. Koronel 《Israel Journal of Mathematics》1976,24(2):119-138
The paper gives a necessary and sufficient condition for the embedding of the Orlicz-Sobolev spaceW
kLA (Ω) inC(Ω). The same condition is also found to be necessary and sufficient so that a continuous function inW
kLA (Ω) be differentiable of orderk almost everywhere in Ω. 相似文献
4.
A. Bonilla F. Pérez-González A. Stray R. Trujillo-González 《Journal d'Analyse Mathématique》1997,73(1):65-89
This paper is concerned with several approximation problems in the weighted Hardy spacesH
p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH
p(Ω) coincides, moduloH
p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan
sets forH
p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer
functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH
p(D), 1 ⪯p < ∞.
Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday. 相似文献
5.
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
6.
Let m be a v-moderate function defined on R
d
and let g ∈ L
2(R
d
). In this work, we defineΩ
m
p
(R
d
) to be the vector space of f ∈ L
m
2
(R
d
) such that the Gabor transform V
f
belongs to L
p
(R
2d
), where 1 ≤ p < ∞. We equip it with a norm and show that it is a Banach space with this norm. We also study some preliminary properties
of Ω
m
p
(R
d
). We also discuss inclusion properties and obtain the dual space of Ω
m
p
(R
d
). At the end of this work, we study multipliers from L
w
1
(R
d
) into Ω
w
p
(R
d
) and from Ω
w
p
(R
d
) into L
w−1
∞
(R
d
), where w is the Beurling weight function.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 139–145, January, 2006. 相似文献
7.
Pankaj K. Agarwal Herbert Edelsbrunner Otfried Schwarzkopf Emo Welzl 《Discrete and Computational Geometry》1991,6(1):407-422
We present an algorithm to compute a Euclidean minimum spanning tree of a given setS ofN points inE
d
in timeO(F
d
(N,N) log
d
N), whereF
d
(n,m) is the time required to compute a bichromatic closest pair amongn red andm green points inE
d
. IfF
d
(N,N)=Ω(N
1+ε), for some fixed ɛ>0, then the running time improves toO(F
d
(N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected timeO((nm logn logm)2/3+m log2
n+n log2
m) inE
3, which yields anO(N
4/3 log4/3
N) expected time, algorithm for computing a Euclidean minimum spanning tree ofN points inE
3. Ind≥4 dimensions we obtain expected timeO((nm)1−1/([d/2]+1)+ε+m logn+n logm) for the bichromatic closest pair problem andO(N
2−2/([d/2]+1)ε) for the Euclidean minimum spanning tree problem, for any positive ɛ.
The first, second, and fourth authors acknowledge support from the Center for Discrete Mathematics and Theoretical Computer
Science (DIMACS), a National Science Foundation Science and Technology Center under NSF Grant STC 88-09648. The second author's
work was supported by the National Science Foundation under Grant CCR-8714565. The third author's work was supported by the
Deutsche Forschungsgemeinschaft under Grant A1 253/1-3, Schwerpunktprogramm “Datenstrukturen und effiziente Algorithmen”.
The last two authors' work was also partially supported by the ESPRIT II Basic Research Action of the EC under Contract No.
3075 (project ALCOM). 相似文献
8.
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
9.
Shi Jihuai 《数学学报(英文版)》1994,10(1):11-18
In this paper, the spaceD
p(Ω) of functions holomorphic on bounded symmetric domain ofC
n is defined. We prove thatH
p(Ω)⊂D
p(Ω) if 0<p≤2, andD
p(Ω)⊂H
p(Ω) ifp≥2, and both the inclusions are proper. Further, we find that some theorems onH
p(Ω) can be extended to a wider classD
p(Ω) for 0<p≤2. 相似文献
10.
Let Ω be a bounded co.nvex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△ on Ω. Let hrp(Ω) = {f ∈ D'(Ω) :(E)F∈hp(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f→(△)2(Gf) for every f ∈ hrp(Ω) is obtained, where n/(n 1)<p≤1. 相似文献
11.
M. Rudelson 《Israel Journal of Mathematics》1995,89(1-3):189-204
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω
S(ω)oT(ω)dω is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n
α
) for some absolute constantα<1.
We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big
dimension isomorphic to ak-cube.
Research supported in part by a grant of the Israel Academy of Sciences. 相似文献
12.
J. Lindenstrauss proves in [L] thatc
0(Γ) is not quasicomplemented inl
∞(Γ) while H. P. Rosenthal in [R] proves that subspaces, whose dual balls are weak* sequentially compact and weak* separable,
are quasicomplemented inl
∞(Γ). In this note it is proved that weak* separability of the dual is the precise condition determining whether a subspace,
without isomorphic copies ofl
1 and whose dual balls are weak* sequentially compact, is quasicomplemented or not inl
∞(Γ). Especially spaces isomorphic tol
p(Γ), for 1<p<∞, have no quasicomplements inl
∞(Γ) if Γ is uncountable. 相似文献
13.
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
14.
Explosive solutions of elliptic equations with absorption and nonlinear gradient term 总被引:2,自引:0,他引:2
Marius Ghergu Constantin Niculescu Vicenţiu Rădulescu 《Proceedings Mathematical Sciences》2002,112(3):441-451
Letf be a non-decreasing C1-function such that
andF(t)/f
2
a(t)→ 0 ast → ∞, whereF(t)=∫
0
t
f(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu|
a
=p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded. 相似文献
15.
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
16.
Sharp estimates of the point-evaluation functional in weighted Bergman spaces L
p
a
(Ω, dν
α) and for the point-evaluation derivalive functional in Besov spaces B
p
(Ω) are obtained for bounded symmetric domains Ω in ℂ
n
.
Received October 25, 1999, Accepted December 6, 2000 相似文献
17.
Quanhua Xu 《Israel Journal of Mathematics》1995,91(1-3):173-187
Let (Ω,F, P) be a probability space and {F
n}n≥0 a regular increasing sequence of sub-σ-fields ofF. LetH
1(Ω) be the usual Hardy space ofF
n-martingales. We show that the couple (H
1(Ω),L
∞(Ω)) is a partial retract of (L
1(Ω),L
∞(Ω)). It is also proved that (L
p(Ω),BMO(Ω)) is a partial retract of (L
p(Ω),L
∞(Ω)) for all 1<p<∞. 相似文献
18.
E. J. Gómez Ayala 《manuscripta mathematica》1994,83(1):199-213
LetK be an imaginary quadratic field with discriminantd
K
<−4,d
K
≡2, 3 mod 4, andp a prime number,p≡1 mod 8,p split inK; let Ω
p
be the ring class field overK with conductorp andK(p) the ray class field overK with conductorp. An explicit normal basis is constructed for the ring of integers of the unique quadratic extension of Ω
p
contained inK(p) over the ring of integers of Ω
p
. This uses certain classical modular units considered by Deuring and Hecke.
相似文献
19.
Domain constants are numbers attached to regions in the complex plane ℂ. For a region Ω in ℂ, letd(Ω) denote a generic domain constant. If there is an absolute constantM such thatM
−1≤d(Ω)/d(Δ)≤M whenever Ω and Δ are conformally equivalent, then the domain constant is called quasiinvariant under conformal mappings.
IfM=1, the domain constant is conformally invariant. There are several standard problems to consider for domain constants. One
is to obtain relationships among different domain constants. Another is to determine whether a given domain constant is conformally
invariant or quasi-invariant. In the latter case one would like to determine the best bound for quasi-invariance. We also
consider a third type of result. For certain domain constants we show there is an absolute constantN such that |d(Ω)−d(Δ)|≤N whenever Ω and Δ and conformally equivalent, sometimes determing the best possible constantN. This distortion inequality is often stronger than quasi-invariance. We establish results of this type for six domain constants.
Research partially supported by a National Science Foundation Grant. 相似文献
20.
In this paper, we consider the global existence, uniqueness and L
∞ estimates of weak solutions to quasilinear parabolic equation of m-Laplacian type u
t
− div(|∇u|
m−2∇u) = u|u|
β−1 ∫Ω |u|
α
dx in Ω × (0,∞) with zero Dirichlet boundary condition in tdΩ. Further, we obtain the L
∞ estimate of the solution u(t) and ∇u(t) for t > 0 with the initial data u
0 ∈ L
q
(Ω) (q > 1), and the case α + β < m − 1. 相似文献