共查询到20条相似文献，搜索用时 328 毫秒
1.
Generalised twists,stationary loops,and the Dirichlet energy over a space of measure preserving maps
M. S. Shahrokhi-Dehkordi A. Taheri 《Calculus of Variations and Partial Differential Equations》2009,35(2):191-213
Let be a bounded Lipschitz domain and consider the Dirichlet energy functional
over the space of measure preserving maps
In this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler–Lagrange equations associated with over . The main result here is that in even dimensions the latter equations admit infinitely many solutions, modulo isometries, amongst such maps. We investigate various qualitative properties of these solutions in view of a remarkably interesting
previously unknown explicit formula. 相似文献
2.
For positive integers with a
r
= 2, the multiple zeta value or r-fold Euler sum is defined as [2]
. There is a celebrated sum formula [6, 10] among multiple zeta values as
,
where range over all positive integers with in the summation.
In this paper, we shall prove the so called restricted sum formula [4]. Namely, for all positive integers m and q with m ≥ q and a nonnegative integer p, that
. We prove the assertion by new expressions of multiple zeta values in terms of Drinfeld integrals.
This work was supported by the Department of Mathematics, National Chung Cheng University and by the National Science Council
of Taiwan, Republic of China. 相似文献
3.
4.
Simon Raulot 《Mathematische Zeitschrift》2009,261(2):321-349
Let M be an n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric g, a spin structure σ and a chirality operator Γ. We define and study some properties of a spin conformal invariant given by:
where is the smallest eigenvalue of the Dirac operator under the chiral bag boundary condition . More precisely, we show that if n ≥ 2 then:
相似文献
5.
Nicola Garofalo 《manuscripta mathematica》2008,126(3):353-373
We prove some new a priori estimates for H
2-convex functions which are zero on the boundary of a bounded smooth domain Ω in a Carnot group . Such estimates are global and are geometric in nature as they involve the horizontal mean curvature of ∂Ω. As a consequence of our bounds we show that if has step two, then for any smooth H
2-convex function in vanishing on ∂Ω one has
.
Supported in part by NSF Grant DMS-07010001. 相似文献
6.
Lei Fu 《Mathematische Zeitschrift》2009,262(2):449-472
Let k be a finite field of characteristic p, l a prime number different from p, a nontrivial additive character, and a character on . Then ψ defines an Artin-Schreier sheaf on the affine line , and χ defines a Kummer sheaf on the n-dimensional torus . Let be a Laurent polynomial. It defines a k-morphism . In this paper, we calculate the weights of under some non-degeneracy conditions on f. Our results can be used to estimate sums of the form
where are multiplicative characters, is a nontrivial additive character, and f
1 , . . . , f
m
, f are Laurent polynomials.
The research is supported by the NSFC (10525107). 相似文献
7.
Yury M. Arlinskiĭ Seppo Hassi Henk S. V. de Snoo 《Complex Analysis and Operator Theory》2009,3(1):19-56
Passive systems with and as an input and output space and as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given
and a general unitary similarity result involving some spectral theoretic conditions on the main operator is established.
A passive system with is said to be quasi-selfadjoint if ran . The subclass of the Schur class is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function
belonging to the subclass and the Q-function of T is given.
Received: December 16, 2007., Accepted: March 4, 2008. 相似文献
8.
Gelu Popescu 《Mathematische Annalen》2008,342(1):1-30
In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna–Pick interpolation problem for
analytic functions with positive real parts on the open unit disc. Given a function , where is an arbitrary subset of the open unit ball , we find necessary and sufficient conditions for the existence of a free holomorphic function g with complex coefficients on the noncommutative open unit ball such that
where is the algebra of all bounded linear operators on a Hilbert space . The proof employs several results from noncommutative multivariable operator theory and a noncommutative Cayley transform
(introduced and studied in the present paper) acting from the set of all free holomorphic functions with positive real parts
to the set of all bounded free holomorphic functions. All the results of this paper are obtained in the more general setting
of free holomorphic functions with operator-valued coefficients. As consequences, we deduce some results concerning operator-valued
analytic interpolation on the unit ball .
Research supported in part by an NSF grant. 相似文献
9.
Zhaoli Liu Jiabao Su Zhi-Qiang Wang 《Calculus of Variations and Partial Differential Equations》2009,35(4):463-480
In this paper, we study existence of nontrivial solutions to the elliptic equation
and to the elliptic system
where Ω is a bounded domain in with smooth boundary ∂Ω, , f (x, 0) = 0, with m ≥ 2 and . Nontrivial solutions are obtained in the case in which the nonlinearities have linear growth. That is, for some c > 0, for and , and for and , where I
m
is the m × m identity matrix. In sharp contrast to the existing results in the literature, we do not make any assumptions at infinity
on the asymptotic behaviors of the nonlinearity f and .
Z. Liu was supported by NSFC(10825106, 10831005). J. Su was supported by NSFC(10831005), NSFB(1082004), BJJW-Project(KZ200810028013)
and the Doctoral Programme Foundation of NEM of China (20070028004). 相似文献
10.
C. Buşe A. D. R. Choudary S. S. Dragomir M. S. Prajea 《Integral Equations and Operator Theory》2008,61(3):325-340
A result of Barbashin ([1], [15]) states that an exponentially bounded evolution family defined on a Banach space and satisfying some measurability conditions is uniformly exponentially stable if and only if for
some 1 ≤ p < ∞, we have that:
Actually the Barbashin result was formulated for non-autonomous differential equations in the framework of finite dimensional
spaces. Here we replace the above ”uniform” condition be a ”strong” one.
Among others we shall prove that the evolution family is uniformly exponentially stable if there exists a non-decreasing function with for all r > 0 such that for each , one has:
In particular, the family U is uniformly exponentially stable if and only if for some 0 < p < ∞ and each , the inequality
is fulfilled. The latter result extends a similar one from the recent paper [4]. Related results for periodic evolution families
are also obtained.
相似文献
11.
Systems of differential equations of the form
with a homeomorphism of the ball are considered, under various boundary conditions on a compact interval [0, T]. For non-homogeneous Cauchy, terminal and some Sturm–Liouville boundary conditions including in particular the Dirichlet–Neumann
and Neumann–Dirichlet conditions, existence of a solution is proved for arbitrary continuous right-hand sides f. For Neumann boundary conditions, some restrictions upon f are required, although, for Dirichlet boundary conditions, the restrictions are only upon and the boundary values. For periodic boundary conditions, both and f have to be suitably restricted. All the boundary value problems considered are reduced to finding a fixed point for a suitable
operator in a space of functions, and the Schauder fixed point theorem or Leray–Schauder degree are used. Applications are
given to the relativistic motion of a charged particle in some exterior electromagnetic field.
Cordially dedicated to Felix Browder for his eightieth birthday anniversary 相似文献
12.
Arrigo Cellina Mihai Vornicescu 《Calculus of Variations and Partial Differential Equations》2009,35(2):263-270
In this paper we establish an existence and regularity result for solutions to the problem
for boundary data that are constant on each connected component of the boundary of Ω. The Lagrangean L belongs to a class that contains both extended valued Lagrangeans and Lagrangeans with linear growth. Regularity means that
the solution is Lipschitz continuous and that, in addition, is bounded. 相似文献
13.
Jérôme Droniou Juan-Luis Vázquez 《Calculus of Variations and Partial Differential Equations》2009,34(4):413-434
We study the existence and uniqueness of solutions of the convective–diffusive elliptic equation
posed in a bounded domain , with pure Neumann boundary conditions
Under the assumption that with p = N if N ≥ 3 (resp. p > 2 if N = 2), we prove that the problem has a solution if ∫Ω
f
dx = 0, and also that the kernel is generated by a function , unique up to a multiplicative constant, which satisfies a.e. on Ω. We also prove that the equation
has a unique solution for all ν > 0 and the map is an isomorphism of the respective spaces. The study is made in parallel with the dual problem, with equation
The dependence on the data is also examined, and we give applications to solutions of nonlinear elliptic PDE with measure
data and to parabolic problems. 相似文献
14.
We prove the following statement.
Let , and let . Suppose that, for all and , the sequence satisfies the relation
where e(u) : = e2πiu
.
Then
where
q is the set of q-multiplicative functions g such that . 相似文献
15.
Boumediene Abdellaoui Veronica Felli Ireneo Peral 《Calculus of Variations and Partial Differential Equations》2009,34(1):97-137
We study the existence of different types of positive solutions to problem
where , , and is the critical Sobolev exponent. A careful analysis of the behavior of Palais-Smale sequences is performed to recover compactness
for some ranges of energy levels and to prove the existence of ground state solutions and mountain pass critical points of the associated functional on the Nehari manifold. A variational perturbative method is also used to study
the existence of a non trivial manifold of positive solutions which bifurcates from the manifold of solutions to the uncoupled
system corresponding to the unperturbed problem obtained for ν = 0.
B. Abdellaoui and I. Peral supported by projects MTM2007-65018, MEC and CCG06-UAM/ESP-0340, Spain. V. Felli supported by Italy
MIUR, national project Variational Methods and Nonlinear Differential Equations. 相似文献
16.
On a periodic boundary value problem for cyclic feedback type linear functional differential systems
Sulkhan Mukhigulashvili 《Archiv der Mathematik》2006,87(3):255-260
Nonimprovable effective sufficient conditions are established for the unique solvability of the periodic problem
where ω > 0, ℓi : C([0, ω])→ L([0,ω]) are linear bounded operators, and qi∈L([0, ω]).
Received: 11 June 2005 相似文献
17.
Ilia Krasikov 《Constructive Approximation》2008,28(2):113-125
T. Erdelyi, A.P. Magnus and P. Nevai conjectured that for
the orthonormal Jacobi polynomials
satisfy the inequality
[Erdelyi et al., Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials. SIAM J. Math. Anal., 25 (1994),
602-614.]. Here we will confirm this conjecture in the ultraspherical case
even in a stronger form by giving very explicit upper bounds. We also show that
for a certain choice of
such that the interval
contains all the zeros of
Slightly weaker bounds are given for polynomials of odd degree. 相似文献
18.
For a trigonometric series
defined on [−π, π)
m
, where V is a certain polyhedron in R
m
, we prove that
if the coefficients a
k
satisfy the following Sidon-Telyakovskii-type conditions:
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 579–585, May, 2008. 相似文献
19.
Robert Černý 《Calculus of Variations and Partial Differential Equations》2007,28(2):203-216
We compute the relaxation
where
for sequences of functions from
converging strongly in the
-norm to
. 相似文献
20.
Xiaomei Wu 《分析论及其应用》2008,24(2):139-148
Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi＞0,m∑I=1βi=β,0＜β＜1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn). 相似文献