共查询到20条相似文献,搜索用时 187 毫秒
1.
We derive the explicit fundamental solutions for a class of degenerate (or singular) one-parameter subelliptic differential operators on groups of Heisenberg (H) type. This extends the results of Kaplan of the sub-Laplacian on H-type groups, which in turn generalizes Folland's result on the Heisenberg group. As an application, we obtain a one-parameter representation formula for Sobolev functions of compact support on H-type groups. By choosing the parameter equal to the homogeneous dimension Q and using the Moser-Trudinger inequality for the convolutional type operator on stratified groups obtained in [18], we get the following theorem which gives the best constant for the Moser-Trudinger inequality for Sobolev functions in H-type groups. Let ${\Bbb G}We derive the explicit fundamental solutions for a class of degenerate (or singular) one-parameter subelliptic differential
operators on groups of Heisenberg (H) type. This extends the results of Kaplan of the sub-Laplacian on H-type groups, which
in turn generalizes Folland's result on the Heisenberg group. As an application, we obtain a one-parameter representation
formula for Sobolev functions of compact support on H-type groups. By choosing the parameter equal to the homogeneous dimension
Q and using the Moser-Trudinger inequality for the convolutional type operator on stratified groups obtained in [18], we get
the following theorem which gives the best constant for the Moser-Trudinger inequality for Sobolev functions in H-type groups.
Let ? be any group of Heisenberg type whose Lie algebra is g enerated by m left invariant vector fields and with a q-dimensional center. Let and
Then,
with A
Q
as the sharp constant, where ∇? denotes the subellitpic gradient on ?
This continues the research originated in our earlier study of the best constants in Moser-Trudinger inequalities and fundamental
solutions for one-parameter subelliptic operators on the Heisenberg group [18].
Received March 15, 2001, Accepted September 21, 2001 相似文献
2.
Bang-Yen Chen 《Monatshefte für Mathematik》2001,134(2):103-119
A CR-submanifold N of a Kaehler manifold is called a CR-warped product if N is the warped product of a holomorphic submanifold and a totally real submanifold of . This notion of CR-warped products was introduced in part I of this series. It was proved in part I that every CR-warped product in a Kaehler manifold satisfies a basic inequality: . The classification of CR-warped products in complex Euclidean space satisfying the equality case of the inequality is archived in part I. The main
purpose of this second part of this series is to classify CR-warped products in complex projective and complex hyperbolic spaces which satisfy the equality.
(Received 13 March 2001; in revised form 10 August 2001) 相似文献
3.
Hiroki Miyahara 《代数通讯》2013,41(2):406-430
We study Gorenstein dimension and grade of a module M over a filtered ring whose associated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the most valuable property for an investigation of filtered rings. We prove an inequality G?dim M ≤ G?dim gr M and an equality grade M = grade gr M, whenever Gorenstein dimension of gr M is finite (Theorems 2.3 and 2.8). We would say that the use of G-dimension adds a new viewpoint for studying filtered rings and modules. We apply these results to a filtered ring with a Cohen–Macaulay or Gorenstein associated graded ring and study a Cohen–Macaulay, perfect, or holonomic module. 相似文献
4.
Hiroyuki Chihara 《Mathematische Annalen》1999,315(4):529-567
We discuss local existence and gain of regularity for semilinear Schr?dinger equations which generally cause loss of derivatives.
We prove our results by advanced energy estimates. More precisely, block diagonalization and Doi's transformation, together
with symbol smoothing for pseudodifferential operators with nonsmooth coefficients, apply to systems of Schr?dinger-type equations.
In particular, the sharp G?rding inequality for pseudodifferential operators whose coefficients are twice continuously differentiable,
plays a crucial role in our proof.
Received: 14 December 1998 相似文献
5.
Jeffrey D. Vaaler 《Monatshefte für Mathematik》2008,154(4):323-343
We prove an upper bound for the Mahler measure of the Wronskian of a collection of N linearly independent polynomials with complex coefficients. If the coefficients of the polynomials are algebraic numbers
we obtain an inequality for the absolute Weil heights of the roots of the polynomials. This later inequality is analogous
to the abc inequality for polynomials, and also has applications to Diophantine problems.
Research supported in part by the National Science Foundation (DMS-06-03282) and the Erwin Schr?dinger Institute.
Author’s address: Department of Mathematics, University of Texas, Austin, Texas 78712, USA 相似文献
6.
S. A. Iskhokov 《Mathematical Notes》2010,87(1-2):189-203
In this paper, we prove Gårding’s weighted inequality for degenerate elliptic operators in an arbitrary (bounded or unbounded) domain of n-dimensional Euclidean space ? n and use this inequality to study the unique solvability of a specific variational problem. It is assumed that the lower coefficients of the operators under consideration belong to some weighted L p -spaces. 相似文献
7.
We prove that the suitably rescaled density matrix of ground states of atomic Schr?dinger operators with nuclear chargeZ converges on the scale 1/Z to the projection of the negative spectral subspace of the Schr?dinger operator of the hydrogen atom (Z=1).
Received March 9, 2000 / Published online February 5, 2001 相似文献
8.
Let N⊂ℝr be a lattice, and let deg:N→ℂ be a piecewise-linear function that is linear on the cones of a complete rational polyhedral fan. Under certain conditions
on deg, the data (N,deg) determines a function f:ℌ→ℂ that is a holomorphic modular form of weight r for the congruence subgroup Γ1(l). Moreover, by considering all possible pairs (N ,deg), we obtain a natural subring ? (l) of modular forms with respect to Γ1 (l). We construct an explicit set of generators for ? (l), and show that ? (l) is stable under the action of the Hecke operators. Finally, we relate ? (l) to the Hirzebruch elliptic genera that are modular with respect to Γ1 (l).
Oblatum 22-IX-1999 & 18-X-2000?Published online: 5 March 2001 相似文献
9.
Dongho Chae 《偏微分方程通讯》2013,38(3):535-557
In this paper we prove nonexistence of stationary weak solutions to the Euler–Poisson equations and the Navier–Stokes–Poisson equations in ? N , N ≥ 2, under suitable assumptions of integrability for the density, velocity and the potential of the force field. For the time dependent Euler–Poisson equations we prove nonexistence result assuming additionally temporal asymptotic behavior near infinity of the second moment of density. For a class of time dependent Navier–Stokes–Poisson equations in ? N this asymptotic behavior of the density can be proved if we assume the standard energy inequality, and therefore the nonexistence of global weak solution follows from more plausible assumption in this case. 相似文献
10.
Using the theory of Sobolev spaces on a metric measure space we are able to apply calculus of variations and define p-harmonic functions as minimizers of the p-Dirichlet integral. More generally, we study regularity properties of quasi-minimizers of p-Dirichlet integrals in a metric measure space. Applying the De Giorgi method we show that quasi-minimizers, and in particular
p-harmonic functions, satisfy Harnack's inequality, the strong maximum principle, and are locally H?lder continuous, if the
space is doubling and supports a Poincaré inequality.
Received: 12 May 2000 / Revised version: 20 April 2001 相似文献
11.
Entropic proximal decomposition methods for convex programs and variational inequalities 总被引:2,自引:0,他引:2
We consider convex optimization and variational inequality problems with a given separable structure. We propose a new decomposition
method for these problems which combines the recent logarithmic-quadratic proximal theory introduced by the authors with a
decomposition method given by Chen-Teboulle for convex problems with particular structure. The resulting method allows to
produce for the first time provably convergent decomposition schemes based on C
∞ Lagrangians for solving convex structured problems. Under the only assumption that the primal-dual problems have nonempty
solution sets, global convergence of the primal-dual sequences produced by the algorithm is established.
Received: October 6, 1999 / Accepted: February 2001?Published online September 17, 2001 相似文献
12.
13.
We study three elliptic problems depending on two small parameters (? = homogenization parameter and δ = perturbation parameter which causes non uniform ellipticity). In each case, the homogenized operator corresponding to the second order operator is independent of the way (?, δ) → (0, 0), but the convergence results and the limit solution do depend on the relative size of ? and δ; the relevant parameter is δ??2. 相似文献
14.
Let N be a finitely generated module over a Noetherian local ring (R,m). We give criteria for the height of the order ideal N*(x) of an element x N to be bounded by the rank of N. The Generalized Principal Ideal Theorem of Bruns, Eisenbud and Evans says that this inequality always holds if x mN. We show that the inequality even holds if the hypothesis becomes true after first extending scalars to some local domain and then factoring out torsion. We give other conditions in terms of residual intersections and integral closures of modules. We derive information about order ideals that leads to bounds on the heights of trace ideals of modules—even in circumstances where we do not have the expected bounds for the heights of the order ideals!All three authors were partially supported by the NSF.Revised version: 24 November 2003 相似文献
15.
Sergio Campanato 《Milan Journal of Mathematics》1990,60(1):113-131
Denoting byu a vector in R
N
defined on a bounded open set Ω ⊂ R
n
, we setH(u)={Dij u} and consider a basic differential operator of second ordera(H(u)) wherea(ξ) is a vector in R
N
, which is elliptic in the sense that it satisfies the condition (A). After a rapid comparison between this condition (A) and the classical definition of ellipticity, we shall prove that, if seu∈H
2 (Ω) is a solution of the elliptic systema(H(u))=0 in Ω thenH(u)∈H
loc
2, q
for someq>2. We then deduce from this the so called fundamental internal estimates for the matrixH(u) and for the vectorsDu andu.
We shall then present a first risult on h?lder regularity for the solutions of the system withf h?lder continuous in Ω, and a partial h?lder continuity risult for solutionsu∈H
2 (Ω) of a differential systema (x, u, Du, H (u))=b(x, u, Du) 相似文献
16.
Hiraku Nakajima 《Inventiones Mathematicae》2001,146(2):399-449
17.
We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted
L
p
-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine
the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a formula for the
relative index.
Mathematics Subject Classifications (2000): Primary 58J32; Secondary 35G70, 35S15. 相似文献
18.
We present a randomized procedure for rounding fractional perfect matchings to (integral) matchings. If the original fractional
matching satisfies any linear inequality, then with high probability, the new matching satisfies that linear inequality in
an approximate sense. This extends the well-known LP rounding procedure of Raghavan and Thompson, which is usually used to
round fractional solutions of linear programs.?We use our rounding procedure to design an additive approximation algorithm
to the Quadratic Assignment Problem. The approximation error of the algorithm is εn
2 and it runs in n
O
(log
n
/ε2) time.?We also describe Polynomial Time Approximation Schemes (PTASs) for dense subcases of many well-known NP-hard arrangement
problems, including MINIMUM LINEAR ARRANGEMENT, MINIMUM CUT LINEAR ARRANGEMENT, MAXIMUM ACYCLIC SUBGRAPH, and BETWEENNESS.
Received: December 12, 1999 / Accepted: October 25, 2001?Published online February 14, 2002 相似文献
19.
The “Projective Rank” of a compact connected irreducible Hermitian symmetric space M has been defined as the maximal complex dimension of the compact totally geodesic complex submanifolds having positive holomorphic bisectional curvature with the induced K?hler metric. We present a geometric way to compute this
invariant for the space M based on ideas developed in [1], [13] and [14]. As a consequence we obtain the following inequality relating the Projective Rank,
the usual rank, and the 2-number (which is known to be equal to the Euler-Poincare characteristic in these spaces).
Received: 6 June 2000 / Revised version: 6 August 2001 / Published online: 4 April 2002 相似文献
20.
《Quaestiones Mathematicae》2013,36(2):195-199
ABSTRACT Poincaré's inequality is well known: given a bounded domain G, ∥u∥p ? c∥?u∥p provided u(x) vanishes on the boundary ?G. The case where u(x) is a vector field u(x) that does not vanish on the boundary ?G is considered. It is shown that when either the tangential component or the normal component vanishes on the boundary ?G, then the Poincaré inequality is satisfied. 相似文献