共查询到20条相似文献,搜索用时 531 毫秒
1.
Yongdo Lim 《Mathematische Annalen》2001,319(3):457-468
Let V be a Euclidean Jordan algebra, and let be the corresponding symmetric cone. The geometric mean of two elements a and b in is defined as a unique solution, which belongs to of the quadratic equation where P is the quadratic representation of V. In this paper, we show that for any a in the sequence of iterate of the function defined by converges to a. As applications, we obtain that the geometric mean of can be represented as a limit of successive iteration of arithmetic means and harmonic means, and we derive the L?wner-Heinz
inequality on the symmetric cone Furthermore, we obtain a formula which leads a Golden-Thompson type inequality for the spectral norm on V.
Received October 5, 1999 / Revised March 6, 2000 / Published online October 30, 2000 相似文献
2.
John Urbas 《Calculus of Variations and Partial Differential Equations》2001,12(4):417-431
In previous work we showed that weak solutions in of the k-Hessian equation have locally bounded second derivatives if g is positive and sufficiently smooth and p > kn/2. Here we improve this result to p > k(n-1)/2, which is known to be sharp in the Monge-Ampère case k=n > 2.
Received June 21, 1999 / Accepted June 12, 2000 / Published online November 9, 2000 相似文献
3.
The equation with boundary Dirichlet zero data is considered in a bounded domain . Under the assumption that concentrates, as , round a manifold and that f is a superlinear function, satisfying suitable growth assumptions, the existence of multiple distinct positive solutions
is proved.
Received: 19 December 2000 / Accepted: 8 May 2001 / Published online: 5 September 2002 相似文献
4.
Improved estimates on the constants L
γ,d
, for 1/2<γ<3/2, d∈N, in the inequalities for the eigenvalue moments of Schr?dinger operators are established.
Oblatum 18-VI-1999 & 13-I-2000?Published online: 29 March 2000 相似文献
5.
M.A. Sychev 《Calculus of Variations and Partial Differential Equations》2001,13(2):213-229
Given a compact set we consider the differential inclusion
We show how to use the main idea of the method of convex integration [ N], [G], [K] (to control convergence of the gradients of a sequence of approximate solutions by appropriate selection of the sequence)
to obtain an optimal existence result. We compare this result with the ones available by the Baire category approach applied
to the set of admissible functions with topology.
A byproduct of our result is attainment in the minimization problems
with integrands L having quasiaffine quasiconvexification that was, in fact, the reason of our interest to differential inclusions. This result
can be considered as a first step towards characterization of those minimization problems which are solvable for all boundary
data. This problem was solved in [S1] in the scalar case m=1.
Received November 5, 1998 / Accepted July 17, 2000 / Published online December 8, 2000 相似文献
6.
Silvia Cingolani José Luis Gámez 《Calculus of Variations and Partial Differential Equations》2000,11(1):97-117
We study a symmetric semilinear elliptic problem in all and we prove existence of an asymmetric positive solution by using variational arguments. The corresponding problem in dimension
N=2, which provides the motivation of this work, arises in Nonlinear Optics from the study of the behaviour of optical cylindrical
waveguides.
Received September 28, 1999/ Accepted January 14, 2000 / Published online June 28, 2000 相似文献
7.
F. Brock V. Ferone B. Kawohl 《Calculus of Variations and Partial Differential Equations》1996,4(6):593-599
Let be a ball in N, centered at zero, and letu be a minimizer of the nonconvex functional
over one of the classesC
M
:= {w W
loc
1,
() 0 w(x) M in,w concave} orE
M
:= {w W
loc
1,2
() 0 w(x) M in,w
0 inL()}of admissible functions. Thenu is not radial and not unique. Therefore one can further reduce the resistance of Newton's rotational body of minimal resistance through symmetry breaking. 相似文献
8.
A. Henrot G. A. Philippin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):784-796
This paper deals with some classical boundary value problems defined in the ring-shaped region
$\Omega \backslash\overline{B(R_0)} \subset \Bbb{R}^N$, where
B(R
0)
is the N-ball of radius
R
0
centered at the origin and contained in .
The authors investigate how the geometry of
is affected
by some overdertermined data. In particular they show that
must be nearly spherical if the overdetermined data are
nearly constants. 相似文献
9.
Explicit exact solutions for a new generalized Hamiltonian amplitude equation with nonlinear terms of any order 总被引:1,自引:0,他引:1
Making use of a proper transformation and a generalized ansatz, we consider a new generalized Hamiltonian amplitude equation with nonlinear terms of any order, iux + utt + (|u|p + |u|2p)u + uxt = 0. As a result, many explicit exact solutions, which include kink-shaped soliton solutions, bell-shaped soliton solutions, periodic wave solutions, the combined formal solitary wave solutions and rational solutions, are obtained.Received: April 4, 2002 相似文献
10.
Juan Manfredi Arshak Petrosyan Henrik Shahgholian 《Calculus of Variations and Partial Differential Equations》2002,14(3):359-384
We consider a free boundary problem for the p-Laplacian
describing nonlinear potential flow past a convex profile K with prescribed pressure on the free stream line. The main purpose of this paper is to study the limit as of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the -Laplacian
in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case the limit is given by the distance function.
Received: 10 October 2000 / Accepted: 23 February 2001 / Published online: 19 October 2001 相似文献
11.
We show that for ε small, there are arbitrarily many nodal solutions for the following nonlinear elliptic Neumann problem where Ω is a bounded and smooth domain in ℝ2 and f grows superlinearly. (A typical f(u) is f(u)= a1 u+p – a1 u-p, a1, a2 >0, p, q>1.) More precisely, for any positive integer K, there exists εK>0 such that for 0<ε<εK, the above problem has a nodal solution with K positive local maximum points and K negative local minimum points. This solution has at least K+1 nodal domains. The locations of the maximum and minimum points are related to the mean curvature on ∂Ω. The solutions are constructed as critical points of some finite dimensional reduced energy functional. No assumption on the symmetry, nor the geometry, nor the topology of the domain is needed. 相似文献
12.
In this note we prove that the uniformity of a complete metric space X is characterized by the vector lattice structure of the set U(X) of all uniformly continuous real functions on X.
(Received 3 March 2000; in revised form 29 June 2000) 相似文献
13.
We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution.
In the special case k=2 we deduce that weak solutions in , , have locally H?lder continuous gradients. In the nondegenerate case we also show that weak solutions in , , have locally bounded second derivatives.
Received February 25, 1999 / Accepted June 11, 1999 / Published online April 6, 2000 相似文献
14.
Hydrodynamic large scale limit for the Ginzburg-Landau ∇φ interface model was established in [6]. As its next stage this
paper studies the corresponding large deviation problem. The dynamic rate functional is given by
for h=h(t,θ),t∈[0,T],θ∈?
d
, where σ=σ(u) is the surface tension for mean tilt u∈ℝ
d
. Our main tool is H
−1-method expoited by Landim and Yau [9]. The relationship to the rate functional obtained under the static situation by Deuschel
et al. [3] is also discussed.
Received: 22 February 2000 / Revised version: 19 October 2000 / Published online: 5 June 2001 相似文献
15.
Noga Alon 《Combinatorica》1996,16(3):301-311
It is shown that there exists a positivec so that for any large integerm, any graph with 2m
2edges contains a bipartite subgraph with at least
edges. This is tight up to the constantc and settles a problem of Erdös. It is also proved that any triangle-free graph withe>1 edges contains a bipartite subgraph with at least e/2+c e
4/5 edges for some absolute positive constantc. This is tight up to the constantc.Research supported in part by a USA Israeli BSF grant and by the Fund for Basic Research administered by the Israel Academy of Sciences. 相似文献
16.
Let X indicate the Freudenthal compactification of a rimcompact, completely regular Hausdorff spaceX. In this paper the spacesY which satisfyXYX are characterized. From this a characterization of whenX lies between its locally compact partL(X) and (L(X)) follows. Such spaces necessarily possess a compactification X for whichCl
X
(X–X) is 0-dimensional. Conditions, including those internal toX, are provided which are necessary and sufficient for this property to hold.This research was partially supported by a grant from Moorhead State University. 相似文献
17.
Shu-Yu Hsu 《Mathematische Annalen》2002,323(2):281-318
We will show that if u is the solution of the equation , in is an even function on and is monotone decreasing in on , , where is a monotone increasing function satisfying with being given by and , then the rescaled function , will converge uniformly on every compact subset of to as where .
Received: 25 May 2000 / Revised version: 26 October 2001 / Published online: 28 February 2002 相似文献
18.
Robert L. Jerrard Halil Mete Soner 《Calculus of Variations and Partial Differential Equations》2002,14(2):151-191
We study the Ginzburg-Landau functional
for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation
of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional.
Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001 相似文献
19.
In this paper we study the existence of bounded weak solutions for some nonlinear Dirichlet problems in unbounded domains. The principal part of the operator behaves like the p-laplacian operator, and the lower order terms, which depend on the solution u and its gradient u, have a power growth of order p–1 with respect to these variables, while they are bounded in the x variable. The source term belongs to a Lebesgue space with a prescribed asymptotic behaviour at infinity. 相似文献
20.
In this paper we study the existence of nontrivial solutions for the following system of coupled semilinear Poisson equations:
where is a bounded domain in
We assume that
and the function f is superlinear and with no growth restriction (for example f(s) = s es); then the system has a nontrivial (strong) solution. 相似文献