共查询到20条相似文献,搜索用时 31 毫秒
1.
Alexander Ženíšek 《Applications of Mathematics》2004,49(5):405-413
Extensions from H
1(P) into H
1() (where P ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded. 相似文献
2.
Takashi Noiri 《Acta Mathematica Hungarica》2005,107(4):307-318
Summary New classes of sets called -closed sets and s-closed sets are introduced and studied. Also, we introduce and study -continuous functions and s-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces -T1/2 and -Ts. 相似文献
3.
Lucilla Bassotti Rizza 《Annali di Matematica Pura ed Applicata》1987,148(1):173-205
Summary Let be an open subset of n, Wm() the linear space of m-vector valued functions defined on , G{} a group of orthogonal matrices mapping onto itself and T{T()} a linear representation of order m of G. A suitable groupC(G,T) of linear operators of Wm(), which leads to a general definition of T-invariant linear operator with respect to G, is here introduced. Characterization theorems concerning the linear differential and integral T-invariant operators are also given. When G is a finite group, projection operators are explicitly obtained; they define a «maximal» decomposition of Wm() into a direct sum of subspaces each of them invariant with respect to any T-invariant linear operator of Wm(). Some examples are givenc.
Lavoro eseguito nell'ambito del progetto nazionale di ricerca «Analisi numerica e matematica computazionale» nell'anno 1985–86. 相似文献
Lavoro eseguito nell'ambito del progetto nazionale di ricerca «Analisi numerica e matematica computazionale» nell'anno 1985–86. 相似文献
4.
We consider a sequence of Dirichlet problems for a nonlinear divergent operator A: W
m
1(
s
) [W
m
1(
s
)]* in a sequence of perforated domains
s
. Under a certain condition imposed on the local capacity of the set \
s
, we prove the following principle of compensated compactness:
, where r
s(x) and z
s(x) are sequences weakly convergent in W
m
1() and such that r
s(x) is an analog of a corrector for a homogenization problem and z
s(x) is an arbitrary sequence from
whose weak limit is equal to zero. 相似文献
5.
Salvatore A. Marano 《Set-Valued Analysis》1996,4(3):287-300
Let be a bounded domain in n (n3) having a smooth boundary, let be an essentially bounded real-valued function defined on × h, and let be a continuous real-valued function defined on a given subset Y of Y h. In this paper, the existence of strong solutions u W
2,p (, h) W
o
1,p
(n/2<p<+) to the implicit elliptic equation (–u)=(x,u), with u=(u1, u2, ..., uh) and u=(u
1, u
2, ..., u
h), is established. The abstract framework where the problem is placed is that of set-valued analysis. 相似文献
6.
We prove a convergence theorem and obtain asymptotic (as 0) estimates for a solution of a parabolic initial boundary-value problem in a junction that consists of a domain 0 and a large number N
2 of -periodically located thin cylinders whose thickness is of order = O(N
–1). 相似文献
7.
K. I. Piletskas 《Journal of Mathematical Sciences》1984,25(1):932-948
In the domain 3 with two exits at infinity, 1 = {x:x<g
1(x
3),x
3 > 2} and 2 = {x:0<x
3<g
3(x), x>2}, one investigates the stationary system of Navier-Stokes equations under the boundary condition. One proves existence and uniqueness theorems for the solution of this problem with an infinite Dirichlet integral, under a given flow of the velocity vector across the cross sections of the exits at infinity. As an example one considers the case wheng
i(t) 1.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 110, pp. 180–202, 1981. 相似文献
8.
For a bounded regular Jordan domain in R
2, we introduce and study a new class of functions K() related on its Green function G. We exploit the properties of this class to prove the existence and the uniqueness of a positive solution for the singular nonlinear elliptic equation u+(x,u)=0, in D(), with u=0 on and uC(), where is a nonnegative Borel measurable function in ×(0,) that belongs to a convex cone which contains, in particular, all functions (x,t)=q(x)t
–,>0 with nonnegative functions qK(). Some estimates on the solution are also given. 相似文献
9.
Let T be a homogeneous tree of homogeneity q+1. Let denote the boundary of T, consisting of all infinite geodesics b=[b
0,b
1,b
2,] beginning at the root, 0. For each b, 1, and a0 we define the approach region ,a
(b) to be the set of all vertices t such that, for some j, t is a descendant of b
j
and the geodesic distance of t to b
j
is at most (–1)j+a. If >1, we view these as tangential approach regions to b with degree of tangency . We consider potentials Gf on T for which the Riesz mass f satisfies the growth condition
T
f
p
(t)q
–|t|<, where p>1 and 0<<1, or p=1 and 0<1. For 11/, we show that Gf(s) has limit zero as s approaches a boundary point b within ,a
(b) except for a subset E of of -dimensional Hausdorff measure 0, where H
(E)=sup>0inf
i
q
–|t
i|:E a subset of the boundary points passing through t
i
for some i,|t
i
|>log
q
(1/). 相似文献
10.
We consider the function space B
p
l
() of functionsf(x), defined on the domain of a certain class and characterized by specific differential-difference properties in Lp(). We prove a theorem on the embedding B
p,q
l
() Lq in the case whenl=n/p –n/q >0 and its generalization for vectorl, p, q.Translated from Matematicheski Zametki, Vol. 6, No. 2, pp. 129–138, August, 1969. 相似文献
11.
Torben Maack Bisgaard 《Analysis Mathematica》2001,27(1):37-54
For >2, let Q
+() be the infimum of those q>0 for which the function n epn is positive definite on N
0 for every pq. We shall prove that Q
+()0 as 2. 相似文献
12.
Luigi Ambrosio 《Acta Appl Math》1989,17(1):1-40
We show how it is possible to prove the existence of solutions of the Mumford-Shah image segmentation functional
F(u,K) = \K
[u2 + (u – g)2]dx +
n – 1(K), u W
1,2(\K), K closed in .We use a weak formulation of the minimum problem in a special class SBV() of functions of bounded variation. Moreover, we also deal with the regularity of minimizers and the approximation of F by elliptic functionals defined on Sobolev spaces. In this paper, we have collected the main results of Ambrosio and others. 相似文献
13.
Summary This paper considers the finite element approximation of the semi-definite Neumann problem: –·(u)=f in a curved domain
n
(n=2 or 3),
on and
, a given constant, for dataf andg satisfying the compatibility condition
. Due to perturbation of domain errors (
h
) the standard Galerkin approximation to the above problem may not have a solution. A remedy is to perturb the right hand side so that a discrete form of the compatibility condition holds. Using this approach we show that for a finite element space defined overD
h
, a union of elements, with approximation powerh
k
in theL
2 norm and with dist (,
h
)Ch
k
, one obtains optimal rates of convergence in theH
1 andL
2 norms whether
h
is fitted (
h
D
h
) or unfitted (
h
D
h
) provided the numerical integration scheme has sufficient accuracy.Partially supported by the National Science Foundation, Grant #DMS-8501397, the Air Force Office of Scientific Research and the Office of Naval Research 相似文献
14.
S. V. Shvedenko 《Mathematical Notes》1977,21(4):281-284
The sequence spaceH
P
(z)={{f (zh)}:f H
p} is defined for a fixed sequence Z={zk} of different points of the open unit disk and the Hardy class HP of analytic functions in the disk. For an arbitrary p[1, ) is constructed a point sequence Z= {zk} such that 1h
p(z), but r hp (Z) for r > 1. It follows from a well-known result of L. Carleson that the inclusions r h (Z) for all r[1,] are equivalent.Translated from Matematicheskie Zametki, Vol. 21, No. 4, pp. 503–508, April, 1977. 相似文献
15.
S. B. Vakarchuk 《Ukrainian Mathematical Journal》1992,44(3):283-291
In the spaces of analytic functionsE
q
(), q1, introduced by V. I. Smirnov, where is a bounded simply connected domain in the plane with sufficiently smooth boundary , we obtain order estimates of diameters of the classesW
r
E
p
() (p1, and r is a natural number 2) for distinct p and q.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 324–333, March, 1992. 相似文献
16.
Ya. Sh. Il'yasov 《Mathematical Notes》1998,64(4):471-475
We writef=(g) iff(x)cg(x) with some positive constantc for allx from the domain of functionsf andg. We show that at least (n
2
/r) entries must be changed in an arbitrary (generalized) Hadamard matrix in order to reduce its rank belowr. This improves the previously known bound (n
2/r
2). If we additionally know that the changes are bounded above in absolute value by some numbern/r, then the number of these entries is bounded below by (n
3/(r
2
)), which improves upon the previously known bound (n
2
/
2
).Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 535–540, April, 1998.The research of the first author was supported by the Russian Foundation for Basic Research under grants No. 96-01-00094 and No. 96-15-96102 and by the INTAS Foundation under grant No. 93-1376. The research of the second author was supported by the Russian Foundation for Basic Research under grants No. 96-01-01222 and No. 96-15-96090. 相似文献
17.
Izu Vaisman 《Annals of Global Analysis and Geometry》1990,8(2):137-145
Summary Let (M, J, g) be a compact complex 2-dimensional Hermitian manifold with the Kähler form , and the torsion 1-form defined by d = . In this note we obtain the Euler-Lagrange equations for the variational functionals defined by 2 and d2, whereg runs in the space of all the Hermitian metrics onM. In the first case, the extremals are precisely the Kähler metrics [Gd]. In the second case, we also write down a formula for the second variation.Communicated by J. Szenthe 相似文献
18.
Rafael López 《Annals of Global Analysis and Geometry》2001,20(1):59-75
We study the problem of finding constant mean curvature graphsover a domain of a totally geodesic hyperplane andan equidistant hypersurface Q of hyperbolic space. We findthe existence of graphs of constant mean curvature H overmean convex domains Q and with boundary for –H
< H |h|, where H
> 0 is the mean curvature of the boundary . Here h is the mean curvature respectively of the geodesic hyperplane (h= 0) and of the equidistant hypersurface (0 < |h|< 1). The lower bound on H is optimal. 相似文献
19.
Summary The paper deals with such estimates of the rate of convergence of difference methods, which are compatible with the smoothness of the exact solutionu W
2
m
(),m>0.5, of elliptic equations with mixed derivatives: The error in the norm of the discrete Sobolev spaceW
2
s
(), denoting the set of grid points, is shown to be of the orderO(|h|
m–s), 0s<m. 相似文献
20.
Peter Hellekalek 《Monatshefte für Mathematik》1992,114(3-4):199-208
Leta be irrational and letf:[0,1] be Riemann-integrable with integral zero. Letf
n
(x) denote the Weyl sumf
n
(x):=
k=0
n–1
f({x
k>}),x/[0,1[,n. We prove criteria for the boundedness of the sequence (f
n
)
n1 and discuss the relation of this question to irregularities of the distribution of sequences. 相似文献