共查询到20条相似文献,搜索用时 15 毫秒
1.
We establish convolution and Fourier restriction estimates for a measure on a 3-
surface in R5. 相似文献
2.
The Doppler transform of a vector field $F = (f_1,f_2,f_3)$ on $\mathbb{R}^3$ is defined by \[\displaystyle\mathcal{D}F(x,\omega) = \sum_j\int_\mathbb{R} \omega_j f_j(x+t\omega)\, dt~,\] where $x\in \mathbb{R}^3$ and $\omega \in S^2$ specifies the direction of a line passing through $x$. In practical applications, $\mathcal{D}F$ is known only for a small subset of lines in $\mathbb{R}^3$. In this article, we deal with the case of $\mathcal{D}F$ restricted to all lines passing through a fixed smooth curve. Using techniques from microlocal analysis, we study the problem of recovering the wavefront set of $\mbox{curl}(F)$ from that of the restricted Doppler transform of $F$. 相似文献
3.
For each $n>2$ we construct a convex body
$K\subset {\Bbb R}^3$ and a finite family ${\cal F}$ of disjoint translates
of $K$ such that any $n-1$ members ${\cal F}$ admit a line transversal, but
${\cal F}$ has no line transversal. 相似文献
4.
E. Sh. Gutshabash 《Journal of Mathematical Sciences》2010,168(6):829-836
Various representations of the equation of minimal surface in
\mathbbR3 {\mathbb{R}^3} are considered. Properties of exact solutions are studied, and a procedure of construction the corresponding conservation
laws is suggested. Links between the solutions of this equation and those of the elliptic version of the Monge–Ampere equation
are found. Bibliography: 19 titles. 相似文献
5.
6.
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
7.
In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite element approach with the natural boundary element method to study the weak solvability and Galerkin approximation of a class of nonlinear exterior boundary value problems. The analysis is mainly based on the variational formulation with constraints. We prove the error estimate of the finite element solution and obtain the asymptotic rate of convergence. Finally, we also give a numerical example. 相似文献
8.
M. A. Stepanova 《Journal of Mathematical Sciences》2005,131(1):5428-5437
Let f:S
2 ↬ R
3 be a generic smooth immersion. The skeleton of f is the following triple (Γ, D, p): Γ ⊂ R
3 is the 1-polyhedron of singular points of f, D = f−1(Γ) ⊂ S
2 is also a 1-polyhedron, and p : D → Γ, x ↦ f(x), is the projection. For triples of the form (D,Γ,p), where Γ has at most
four vertices, we give an iff-condition under which the triple is the skeleton of a smooth immersion f : S
2 ↬ R
3. Bibliography: 4 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 300–313. 相似文献
9.
L. P. Plakhta 《Ukrainian Mathematical Journal》2007,59(9):1385-1396
We give a survey of some known results related to combinatorial and geometric properties of finite-order invariants of knots
in a three-dimensional space. We study the relationship between Vassiliev invariants and some classical numerical invariants
of knots and point out the role of surfaces in the investigation of these invariants. We also consider combinatorial and geometric
properties of essential tori in standard position in closed braid complements by using the braid foliation technique developed
by Birman, Menasco, and other authors. We study the reductions of link diagrams in the context of finding the braid index
of links.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1239–1252, September, 2007. 相似文献
10.
We investigate the dynamics of solutions of an autonomous wave equation in ℝn with continuous nonlinearity. A priori estimates are obtained. We substantiate the existence of an invariant global attractor
for an m-semiflow.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 260–267, February, 2008. 相似文献
11.
We generalize results of our previous paper, showing
that the minimal grid of a fenestration of the plane, whose
elements are open discs with frontiers which are Jordan curves,
has Alexandroff dimension 2. We give examples to show why this
condition on the frontier is required and that the methods
employed here are not applicable in higher dimensions. 相似文献
12.
H. Beirão da Veiga 《Mathematische Annalen》2005,331(1):203-217
We give a simple and very complete proof of the existence of a strong (H2) solution to the non-homogeneous problem (1.1) under the non homogeneous boundary conditions (1.6). Here we consider the half-space case = Rn+, n 3, see theorem 1.2. This regularity result was previously obtained by Solonnikov and adilov in reference [33] for the classical Stokes system (==0, g(x)=0) in the 3–D homogenous case (a=0, b=0) and a suitable open subset of R3.Partly supported by CMAF/UL and FCT. 相似文献
13.
A. N. Plyushchenko 《Russian Mathematics (Iz VUZ)》2011,55(11):76-79
We study the word problem for the free Burnside semigroups satisfying x
2 = x
3. For any k > 2, we reduce this problem for the k-generated free Burnside semigroup B(2, 1, k) to the word problem for the two-generated semigroup B(2, 1, 2). Furthermore, if every element of B(2, 1, 2) is a regular language, then every element of B(2, 1, k) appears to be a regular language as well. Thus, Brzozowski’s conjecture holds for the semigroup B(2, 1, k) if and only if it holds for B(2, 1, 2). 相似文献
14.
Dorina Mitrea Marius Mitrea Jill Pipher 《Journal of Fourier Analysis and Applications》1997,3(2):131-192
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems
of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding
theory for Lp-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering. 相似文献
15.
YunYanYANG 《数学学报(英文版)》2003,19(1):63-68
In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions. 相似文献
16.
Tongkeun Chang 《Potential Analysis》2008,29(2):105-117
In this paper, we show the existence of the solutions of the screen problems of the Stokes equation in R
n
, n ≥ 3. For the purpose of it, we use the fractional layer potentials (for the Stokes equation) in a bounded Lipschitz domain
The author is supported by the Korea Research Grant Foundation Grant (MOEHRD)KRF-2005-214-C00179. 相似文献
17.
Andreas Holmsen 《Discrete and Computational Geometry》2007,37(3):341-349
Let F be a family of disjoint translates of a compact convex set in the plane. In 1980 Katchalski and Lewis showed that there
exists a constant k, independent of F, such that if each three members of F are met by a line, then a "large" subfamily G
⊂ F, with |F\G| ≤ k, is met by a line. In this paper we obtain a higher-dimensional analogue containing the Katchalski-Lewis
result. Also we give two constructions of families of pairwise disjoint translates of the unit ball in R3 which answer some related questions. 相似文献
18.
We obtain a priori estimates for solutions to the prescribed scalar curvature equation on S
3. The usual non-degeneracy assumption on the curvature function is replaced by a new condition, which is necessary and sufficient
for the existence of a priori estimates, when the curvature function is a positive Morse function. 相似文献
19.
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
20.
Our aim in this paper is to discuss a Montel type result for a family F{\mathcal F} of super-polyharmonic functions on R
N
. We give a condition on spherical means to assure that F{\mathcal F} contains a sequence converging outside a set of capacity zero. 相似文献