共查询到20条相似文献,搜索用时 640 毫秒
1.
S. I. Lyashko S. O. Voitsekhovskii V. I. Garkusha 《Journal of Mathematical Sciences》2001,107(2):3764-3775
To solve optimal control problems for elliptic systems in domains that have an arbitrary form, we use a combination of the method of dummy domains and the grid method. We show that the proposed difference scheme has precision of order O(h
1/2) with respect to the grid norm of W2
2. 相似文献
2.
S. O. Voitsekhovskii 《Journal of Mathematical Sciences》2001,104(6):1599-1603
In this article, using the method of dummy domains and operators of exact difference schemes, we construct a difference scheme for the first boundary-value problem in elasticity theory. The scheme, for domains of an arbitrary shape, has the order of accuracy O(h1/2)with respect to the norm of W
2
1
(). 相似文献
3.
Hans Christianson 《偏微分方程通讯》2015,40(4):629-651
We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ε0 > 0, an 𝒪(λ?ε0 ) quasimode must have L 2 mass in the “wings” (in phase space) bounded below by λ?2?δ for any δ > 0. The proof uses the author's recent work on 0-Gevrey smooth domains to approximate quasimodes on C 1, 1 domains. There is an improvement for C k, α and C ∞ domains. 相似文献
4.
A family {K
i
| of convex domains in the Euclidean planeR
2 is said to permit a plane covering if there exist rigid motions {τi} such that U
i
∞
=1τi
K
i =R
2. Necessary and sufficient conditions that a given family of convex domains permits a plane covering are established. 相似文献
5.
A. G. Ramm 《Mathematical Methods in the Applied Sciences》1995,18(2):121-126
Let Dj,j = 1,2, be two bounded domains (obstacles) in ?n, n ≥ 2, with the boundaries Γj. Let Aj be the scattering amplitude corresponding to Dj. The Dirichlet boundary condition is assumed on Γj. A formula is derived for A:= A1 ? A2. This formula is used for a derivation of the estimate of ∣A1 ? A2∣ in terms of the distance d(Γ1, Γ2) between Γ1 and Γ2. If d(Gamma;1, Gamma;2) ? ?, then ∣A∣ ? c?, where c is a positive constant which depends on Γ1 and Γ2 provided that one of the boundaries is of C1,λ class, 0 < λ < 1, and the other one is a polyhedron which approximates the first one. The results are useful, in particular, for boundary elements method of solving scattering problems. 相似文献
6.
In previous papers [MS 1, 2], we considered stationary critical points of solutions of the initial-boundary value problems
for the heat equation on bounded domains in ℝN,N ≧ 2. In [MS 1], we showed that a solutionu has a stationary critical pointO if and only ifu satisfies a certain balance law with respect toO for any time. Furthermore, we proved necessary and sufficient conditions relating the symmetry of the domain to the initial
datau
0; in this way, we gave a characterization of the ball in ℝN([MS 1]) and of centrosymmetric domains ([MS 2]). In the present paper, we consider a rotationA
dby an angle 2π/d,d ≧ 2 for planar domains and give some necessary and some sufficient conditions onu
0 which relate to domains invariant underA
d. We also establish some conjectures.
This research was partially supported by a Grant-in-Aid for Scientific Research (C) (# 10640175) and (B) (# 12440042) of the
Japan Society for the Promotion of Science. The first author was supported also by the Italian MURST. 相似文献
7.
8.
Dirk Pauly 《Mathematical Methods in the Applied Sciences》2008,31(13):1509-1543
We study in detail Hodge–Helmholtz decompositions in nonsmooth exterior domains Ω??N filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms of rank q belonging to the weighted L2‐space Ls2, q(Ω), s∈?, into irrotational and solenoidal q‐forms. These decompositions are essential tools, for example, in electro‐magnetic theory for exterior domains. To the best of our knowledge, these decompositions in exterior domains with nonsmooth boundaries and inhomogeneous and anisotropic media are fully new results. In the Appendix, we translate our results to the classical framework of vector analysis N=3 and q=1, 2. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
Bodo Dittmar 《Mathematische Nachrichten》2004,268(1):44-49
Let 0 = λ1 < λ2 ≤ λ3 ≤ … be the Stekloff eigenvalues of a plane domain. The paper is concerned with formulas for ∑∞2λ(–2)j in simply and doubly connected domains. In the simply connected case it is proven that the disk minimized this sum. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
David G. Carta 《BIT Numerical Mathematics》1978,18(4):490-492
Rational fractions of the formR(x)/(c
1 +c
2
x +c
3
x
2 + ...)
r
are useful for approximating decay type functions over infinite and semi-infinite domains. A procedure is given which produces the optimal coefficients with no more effort than for linear approximations. No initial guess is needed for the values of the coefficients nor for the maximum error of approximation. 相似文献
11.
Rossella Agliardi 《Annali dell'Universita di Ferrara》1993,39(1):93-109
A well-known example by Ivrii concerning the operatorP=D
t
2
−t2lD
x
2
+atkDx (a≠0), shows that there exists a delicate relation amongl, k and the Gevrey index of well-posedness of the Cauchy problem. In this paper we give a generalization to a class of pseudo-differential
operators includingP.
Sunto Un famoso esempio di Ivrii riguardante l'operatoreP=D t 2 −t2lD x 2 +atkDx (a≠0), mostra che c'è una relazione sottile tral, k e l'indice di Gevrey di buona positura del problema di Cauchy. In questo articolo viene data una generalizzazione ad una classe di operatori pseudodifferenziali che comprendeP.相似文献
12.
In this paper we prove local analyticity of solutions to the
-Neumann problem up to the boundary of rigid, completely decoupled pseudoconvex domains with real-analytic boundary. These
are domains that are locally of the form Imw > Σ |h
k
(z
k
)|2 with eachh
k
holomorphic and vanishing only at 0.
As in those earlier papers, we use purelyL
2 methods and must construct a special holomorphic vector fieldM and then use carefully balanced polynomials inM to localize high powers ofT = ∂/∂t effectively, wheret = Rew. 相似文献
13.
The main purpose is to generalize a theorem of Arendt about uniqueness of C
0-semigroups from Banach space setting to general locally convex vector spaces. More precisely, we show that cores are the
only domains of uniqueness for C
0-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport
equation has one unique L
1(ℝ
d
,dx) weak solution. 相似文献
14.
R. Delaubenfels 《Acta Mathematica Hungarica》2001,92(4):311-324
For B
1 and B
2 commuting linear operators on a Banach space such that B
1 generates a bounded strongly continuous semigroup and –B
2 generates an exponentially decaying strongly continuous holomorphic semigroup, it is shown that (B
1 – B
2)–1
B
2
–r
and (B
1 – B
2)–1(–B
1)–r
are bounded and everywhere defined, for any r > 0. Density of domains may also be removed. The results are applied to various abstract Cauchy problems. 相似文献
15.
Schatten class hankel operators on the Bergman space 总被引:1,自引:0,他引:1
Dechao Zheng 《Integral Equations and Operator Theory》1990,13(3):442-459
In this paper we characterize Hankel operatorsH
f andH
f on the Bergman spaces of bounded symmetric domains which are in the Schatten p-class for 2p< and f inL
2 using a Jordan algebra characterization of bounded symmetric domains and properties of the Bergman metric. 相似文献
16.
A. Boulkhemair 《偏微分方程通讯》2013,38(9):1439-1447
We give a proof of the Poincaré inequality in W 1, p (Ω) with a constant that is independent of Ω ? , where is a set of uniformly bounded and uniformly Lipschitz domains in ? n . As a byproduct, we obtain the following: The first non vanishing eigenvalues λ2(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the domains Ω vary and remain uniformly bounded and uniformly Lipschitz regular. 相似文献
17.
We establish an estimate for the degree of a holomorphic mapping f : K 1 K
2 (here, K
1 and K
2 are doubly-connected domains) in terms of the modulus of a family of curves in K
2. This estimate generalizes a result obtained by Kobayashi.Published in Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1135–1138, August, 2004. 相似文献
18.
19.
S. A. Voitsekhovsky 《Journal of Mathematical Sciences》1995,77(5):3406-3409
Using the dummy-domains method, a difference scheme is constructed for solving the first boundary-value problem for elliptic
equations of the second order in domains of arbitrary shape. An estimate for the convergence rate of order O(h1/2) in the norm of W
2
1
is found. Bibliography:5 titles.
Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 12–18 相似文献
20.
Chang Heon Kim 《The Ramanujan Journal》2010,22(2):187-207
Let p be a prime and f(z)=∑
n
a(n)q
n
be a weakly holomorphic modular function for
\varGamma 0*(p2)\varGamma _{0}^{*}(p^{2}) with a(0)=0. We use Bruinier and Funke’s work to find the generating series of modular traces of f(z) as Jacobi forms. And as an application we construct Borcherds products related to the Hauptmoduln jp2*j_{p^{2}}^{*} for genus zero groups
\varGamma 0*(p2)\varGamma _{0}^{*}(p^{2}). 相似文献