共查询到20条相似文献,搜索用时 15 毫秒
1.
For an n -dimensional compact submanifold Mn in the Euclidean space RN, we study estimates for eigenvalues of the Paneitz operator on Mn. Our estimates for eigenvalues are sharp. 相似文献
2.
Genqian Liu 《Advances in Mathematics》2011,228(4):2162
Let Ω be a bounded domain with C2-smooth boundary in an n-dimensional oriented Riemannian manifold. It is well known that for the biharmonic equation Δ2u=0 in Ω with the condition u=0 on ∂Ω, there exists an infinite set {uk} of biharmonic functions in Ω with positive eigenvalues {λk} satisfying on ∂Ω. In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of the biharmonic Steklov eigenvalues λk. 相似文献
3.
In this paper, we investigate an eigenvalue problem for the Dirichlet Laplacian on a domain in an n-dimensional compact Riemannian manifold. First we give a general inequality for eigenvalues. As one of its applications,
we study eigenvalues of the Laplacian on a domain in an n-dimensional complex projective space, on a compact complex submanifold in complex projective space and on the unit sphere.
By making use of the orthogonalization of Gram–Schmidt (QR-factorization theorem), we construct trial functions. By means
of these trial functions, estimates for lower order eigenvalues are obtained.
Qing-Ming Cheng research was partially supported by a Grant-in-Aid for Scientific Research from JSPS.
Hejun Sun and Hongcang Yang research were partially supported by NSF of China. 相似文献
4.
In this paper, we investigate eigenvalues of the Dirichlet eigenvalue problem of Laplacian on a bounded domain Ω in an n-dimensional complete Riemannian manifold M. When M is an n-dimensional Euclidean space Rn, the conjecture of Pólya is well known: the kth eigenvalue λk of the Dirichlet eigenvalue problem of Laplacian satisfies
5.
For a bounded planar region in R2, we obtain the ratios of lower order eigenvalues of Laplace operator. Combining our results with the recursive formula in Cheng and Yang (2007) [11], we can obtain better upper bound of the (k+1)-th (k?3) membrane eigenvalues. 相似文献
6.
In [C.K. Chui and X.L. Shi, Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal., 24 (1993), 263–277], the authors proved that if
is a Gabor frame for
with frame bounds A and B, then the following two inequalities hold:
and
. In this paper, we show that similar inequalities hold for multi-generated irregular Gabor frames of the form
, where Δ
k
and Λ
k
are arbitrary sequences of points in
and
, 1 ≤ k ≤ r.
Corresponding author for second author
Authors’ address: Lili Zang and Wenchang Sun, Department of Mathematics and LPMC, Nankai University, Tianjin 300071, China 相似文献
7.
Bodo Dittmar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):565-568
For a simply connected and normalized domain D in the plane it was proven by Pólya and Schiffer in 1954 for the fixed membrane eigenvalues
for any n, where λj(0) are the fixed membrane eigenvalues of the unit disk. The purpose of this paper is to prove an analog inequality for the free
membrane eigenvalues.
相似文献
8.
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption u t-u m + γup = 0, where γ≥ 0, m 1 and p m + 2/N . We will show that if γ = 0 and 0 μ 2N/(N(m-1)+2), or γ 0 and 1/(p-1)μ2N/(N(m-1)+2), then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S (R N ), there exists an initial-value u0 ∈C(RN) with lim x →∞ u 0 (x) = 0 such that φ is an ω-limit point of the rescaled solutions t μ/2 u(t β·, t), where β =[2-μ(m-1)]/4 . 相似文献
9.
Rafael María Rubio Ruiz 《manuscripta mathematica》2001,105(3):323-342
By differentiability we means C
∞ differentiability. Recall that the span of a manifold M is the maximum number of linearly independent vector fields in every
point. The aim of this paper is to relate the span of M with the minimal dimension of the orbits of a differentiable action ϕ:ℝ
n
×M→M that keeps a contact structure.
Received: 19 July 2000 / Revised version: 20 April 2001 相似文献
10.
Pablo L. De Nápoli 《Journal of Differential Equations》2006,227(1):102-115
In this paper we introduce the generalized eigenvalues of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many continuous eigencurves, which are obtained by variational methods. For the one-dimensional problem, we obtain an hyperbolic type function defining a region which contains all the generalized eigenvalues (variational or not), and the proof is based on a suitable generalization of Lyapunov's inequality for systems of ordinary differential equations. We also obtain a family of curves bounding by above the kth variational eigencurve. 相似文献
11.
Fa-en WU~ 《中国科学A辑(英文版)》2007,50(8):1078-1086
Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 < λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang. 相似文献
12.
Summary.
New approaches for computing tight lower
bounds to the eigenvalues of a class of
semibounded self-adjoint operators are
presented that require comparatively
little a priori spectral information and permit the
effective use of (among others) finite-element trial functions.
A variant of the method of intermediate problems making use
of operator decompositions having the form
is
reviewed and then developed into a new framework based on
recent inertia results in the Weinstein-Aronszajn theory. This
framework provides greater flexibility in analysis and permits
the formulation of a final computational task involving
sparse, well-structured matrices. Although our derivation is
based on an intermediate problem formulation, our results
may be specialized to obtain either the Temple-Lehmann
method or Weinberger's matrix method.
Received December 12, 1992 / Revised version
received October 5, 1994 相似文献
13.
We study the long-time asymptotics of linear kinetic models with periodic boundary conditions or in a rectangular box with specular reflection boundary conditions. An entropy dissipation approach is used to prove decay to the global equilibrium under some additional assumptions on the equilibrium distribution of the mass preserving scattering operator. We prove convergence at an algebraic rate depending on the smoothness of the solution. This result is compared to the optimal result derived by spectral methods in a simple one dimensional example. 相似文献
14.
The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation
{△^2u + a(x)u = g(x, u)
u∈ H^2(R^N),
where the condition u∈ H^2(R^N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense. 相似文献
{△^2u + a(x)u = g(x, u)
u∈ H^2(R^N),
where the condition u∈ H^2(R^N) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense. 相似文献
15.
László Verhóczki 《Monatshefte für Mathematik》2004,141(4):323-335
In the present paper we discuss in detail the cohomogeneity one isometric actions of the Lie groups SU(3) × SU(3) and SU(3) on the exceptional compact symmetric spaces G2 and G2/SO(4), respectively. We show that the principal orbits coincide with the tubular hypersurfaces around the totally geodesic singular orbits, and the symmetric spaces G2 and G2/SO(4) can be thought of as compact tubes around SU(3) and P2, respectively. Moreover, we determine the radii of these tubes and describe the shape operators of the principal orbits. Finally, we apply these results to compute the volumes of the two symmetric spaces.The author was partially supported by the Hungarian National Science and Research Foundation OTKA T032478. 相似文献
16.
Feng-Yu Wang 《Probability Theory and Related Fields》1995,101(3):363-369
Summary In this note, we adopt a probabilistic method for estimating the first Dirichlet eigenvalue. The results improve or contain some known ones, especially for large dimension. Moreover, our estimates are sharp for some typical cases.Research supported in part by NSFC and the State Education Commission of China 相似文献
17.
This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed. 相似文献
18.
Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞. 相似文献
19.
陈泽乾 《数学物理学报(B辑英文版)》2009,29(5):1225-1232
In this article, we are concerned with the Dirichlet problem of the stationary von Neumann-Landau wave equation:
{(-△x+△y)φ(x,y)=0,x,y∈Ω
φ|δΩxδΩ=f
where Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods. 相似文献
{(-△x+△y)φ(x,y)=0,x,y∈Ω
φ|δΩxδΩ=f
where Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods. 相似文献
20.
We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical
case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.
While the only small self-similar solution in the strong
space is the null solution, infinitely many self-similar solutions do exist in weak-
spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained
in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained. 相似文献