共查询到20条相似文献,搜索用时 968 毫秒
1.
Pavel Drábek Peter Takáč 《Calculus of Variations and Partial Differential Equations》2007,29(1):31-58
An improved Poincaré inequality and validity of the Palais-Smale condition are investigated for the energy functional on , 1 < p < ∞, where Ω is a bounded domain in , is a spectral (control) parameter, and is a given function, in Ω. Analysis is focused on the case λ = λ1, where −λ1 is the first eigenvalue of the Dirichlet p-Laplacian Δ
p
on , λ1 > 0, and on the “quadratization” of within an arbitrarily small cone in around the axis spanned by , where stands for the first eigenfunction of Δ
p
associated with −λ1. 相似文献
2.
We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg
group . The model case is the non-degenerate p-Laplacean operator where , and p is not too far from 2. 相似文献
3.
In this paper, we give an Lp-Lq-version of Morgans theorem for the Dunkl-Bessel transform
on
More precisely, we prove that for all
and
then for all measurable function f on
the conditions
and
imply f = 0, if and only if
where
are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004 相似文献
4.
The Stokes operator in weighted Lq-spaces II: weighted resolvent estimates and maximal Lp-regularity 总被引:1,自引:0,他引:1
Andreas Fr?hlich 《Mathematische Annalen》2007,339(2):287-316
In this paper we establish a general weighted L
q
-theory of the Stokes operator in the whole space, the half space and a bounded domain for general Muckenhoupt weights . We show weighted L
q
-estimates for the Stokes resolvent system in bounded domains for general Muckenhoupt weights. These weighted resolvent estimates
imply not only that the Stokes operator generates a bounded analytic semigroup but even yield the maximal L
p
-regularity of in the respective weighted L
q
-spaces for arbitrary Muckenhoupt weights . This conclusion is archived by combining a recent characterisation of maximal L
p
-regularity by -bounded families due to Weis [Operator-valued Fourier multiplier theorems and maximal L
p
-regularity. Preprint (1999)] with the fact that for L
q
-spaces -boundedness is implied by weighted estimates. 相似文献
5.
Luis J. Alías Marcos Dajczer Harold Rosenberg 《Calculus of Variations and Partial Differential Equations》2007,30(4):513-522
We study constant mean curvature graphs in the Riemannian three- dimensional Heisenberg spaces . Each such is the total space of a Riemannian submersion onto the Euclidean plane with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC graphs in with respect to the Riemannian submersion over certain domains taking on prescribed boundary values.
L. J. Alías was partially supported by MEC/FEDER project MTM2004-04934-C04-02 and Fundación Séneca project 00625/PI/04, Spain. 相似文献
6.
Yuan Zhang 《Mathematische Annalen》2007,337(2):457-478
Let
and
denote the complexifications of Heisenberg hypersurfaces in
and
, respectively. We show that non-degenerate holomorphic Segre mappings from
into
with
possess a partial rigidity property. As an application, we prove that the holomorphic Segre non-transversality for a holomorphic Segre map from
into
with
propagates along Segre varieties. We also give an example showing that this propagation property of holomorphic Segre transversality fails when N > 2n − 2. 相似文献
7.
8.
Olivier Druet Emmanuel Hebey 《Calculus of Variations and Partial Differential Equations》2008,31(2):205-230
Let (M, g) be a smooth compact Riemannian n-manifold, n ≥ 3. Let also p ≥ 1 be an integer, and be the vector space of symmetrical p × p real matrix. We consider critical elliptic systems of equations which we write in condensed form as
where , is a p-map, is the Laplace–Beltrami operator acting on p-maps, and 2* is the critical Sobolev exponent. We fully answer the question of getting sharp asymptotics for local minimal
type solutions of such systems. As an application, we prove compactness of minimal type solutions and prove that the result
is sharp by constructing explicit examples where blow-up occurs when the compactness assumptions are not fulfilled. 相似文献
9.
Let be a lattice of finite height. The correspondence between closure operators and ∧-subsemilattices is well known. Here we investigate what type of number-valued function is induces a ∧-subsemilattice ; and if so, what kind of . Conversely, what type of function is induced by what type of (or cl). Several results known for matroids, greedoids, or semimodular lattices are generalized. 相似文献
10.
Ruben Jakob 《Calculus of Variations and Partial Differential Equations》2007,28(3):383-409
In this paper we derive a sufficient condition for the existence of extremal surfaces of a parametric functional
with a dominant area term, which do not furnish global minima of
within the class
of H
1,2-surfaces spanning an arbitrary closed rectifiable Jordan curve
that merely has to satisfy a chord-arc condition. The proof is based on the “mountain pass result” of (Jakob in Calc Var 21:401–427, 2004) which yields an unstable
-extremal surface bounded by an arbitrary simple closed polygon and Heinz’ ”approximation method” in (Arch Rat Mech Anal 38:257–267,
1970). Hence, we give a precise proof of a partial result of the mountain pass theorem claimed by Shiffman in (Ann Math 45:543–576, 1944) who only outlined a very sketchy and partially incorrect proof. 相似文献
11.
Juan Dávila Manuel del Pino Monica Musso Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2008,32(4):453-480
We consider the elliptic problem Δu + u
p
= 0, u > 0 in an exterior domain, under zero Dirichlet and vanishing conditions, where is smooth and bounded in , N ≥ 3, and p is supercritical, namely . We prove that this problem has infinitely many solutions with slow decay
at infinity. In addition, a solution with fast decay
O(|x|2-N
) exists if p is close enough from above to the critical exponent. 相似文献
12.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
13.
Elena Cordero Stevan Pilipović Luigi Rodino Nenad Teofanov 《Mediterranean Journal of Mathematics》2005,2(4):381-394
We study localization operators within the framework of ultradistributions. More precisely, given a symbol a and two windows φ1, φ2, we investigate the multilinear mapping from
to the localization operator
Results are formulated in terms of modulation spaces with weights which may have exponential growth. We give sufficient and
necessary conditions for
a to be bounded or to belong to a Schatten class. As an application, we study symbols defined by ultra-distributions with
compact support, that give trace class localization operators. 相似文献
14.
The main result of this work is a Dancer-type bifurcation result for the quasilinear elliptic problem
Here, Ω is a bounded domain in denotes the Dirichlet p-Laplacian on , and is a spectral parameter. Let μ1 denote the first (smallest) eigenvalue of −Δ
p
. Under some natural hypotheses on the perturbation function , we show that the trivial solution is a bifurcation point for problem (P) and, moreover, there are two distinct continua, and , consisting of nontrivial solutions to problem (P) which bifurcate from the set of trivial solutions at the bifurcation point (0, μ1). The continua and are either both unbounded in E, or else their intersection contains also a point other than (0, μ1). For the semilinear problem (P) (i.e., for p = 2) this is a classical result due to E. N. Dancer from 1974. We also provide an example of how the union looks like (for p > 2) in an interesting particular case.
Our proofs are based on very precise, local asymptotic analysis for λ near μ1 (for any 1 < p < ∞) which is combined with standard topological degree arguments from global bifurcation theory used in Dancer’s original
work.
Submitted: July 28, 2007. Accepted: November 8, 2007. 相似文献
((P)) |
15.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献
16.
James Gillespie 《Mathematische Zeitschrift》2007,257(4):811-843
We put a monoidal model category structure on the category of chain complexes of quasi-coherent sheaves over a quasi-compact
and semi-separated scheme X. The approach generalizes and simplifies the method used by the author in (Trans Am Math Soc 356(8) 3369–3390, 2004) and
(Trans Am Math Soc 358(7), 2855–2874, 2006) to build monoidal model structures on the category of chain complexes of modules
over a ring and chain complexes of sheaves over a ringed space. Indeed, much of the paper is dedicated to showing that in
any Grothendieck category , any nice enough class of objects induces a model structure on the category Ch() of chain complexes. The main technical requirement on is the existence of a regular cardinal κ such that every object satisfies the following property: Each κ-generated subobject of F is contained in another κ-generated subobject S for which . Such a class is called a Kaplansky class. Kaplansky classes first appeared in Enochs and López-Ramos (Rend Sem Mat Univ Padova 107, 67–79,
2002) in the context of modules over a ring R. We study in detail the connection between Kaplansky classes and model categories. We also find simple conditions to put
on which will guarantee that our model structure is monoidal. We will see that in several categories the class of flat objects
form such Kaplansky classes, and hence induce monoidal model structures on the associated chain complex categories. We will
also see that in any Grothendieck category , the class of all objects is a Kaplansky class which induces the usual (non-monoidal) injective model structure on Ch(). 相似文献
17.
Tyler Lawson 《K-Theory》2006,37(4):395-422
For finitely generated groups G and H, we prove that there is a weak equivalence
G H (G × H) of ku-algebra spectra, where denotes the “unitary deformation K-theory” functor. Additionally, we give spectral sequences for computing the homotopy groups of G and HG in terms of connective K-theory and homology of spaces of G-representations. 相似文献
18.
We prove that on bounded domains Ω, the usual Sobolev inequality for sublaplacians on Carnot groups can be improved by adding
a remainder term, in striking analogy with the euclidean case. We also show analogous results for subelliptic operators like
$$ {\user1{\mathcal{L}}} = \Delta _{x} + |x|^{{2\alpha }} \Delta _{y} ,\,\alpha \gt 0. $$ 相似文献
19.
Assume that 1 ≤ p < ∞ and a function f ∈ L p [0, π] has the Fourier series $ \sum\limits_{n = 1}^\infty {a_n } Assume that 1 ≤ p < ∞ and a function f ∈ L
p
[0, π] has the Fourier series cos nx. According to one result of G.H. Hardy, the series cos nx is the Fourier series for a certain function (f) ∈ L
p
[0, π]. But if 1 < p ≤ ∞ and f ∈ L
p
[0, π], then the series cos nx is the Fourier series for a certain function (f) ∈ L
p
[0, π]. Similar assertions are true for sine series. This allows one to define the Hardy operator on L
p
(), 1 ≤ p < ∞, and to define the Bellman operator on L
p
(), 1 < p ≤ ∞. In this paper we prove that the Bellman operator boundedly acts in VMO(), and the Hardy operator also maps a certain subspace C() onto VMO(). We also prove the invariance of certain classes of functions with given majorants of modules of continuity or best approximations
in the spaces H(), L(), VMO() with respect to the Hardy and Bellman operators.
Original Russian Text ? S.S. Volosivets and B.I. Golubov, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika,
2008, No. 5, pp. 4–13. 相似文献
20.
Zhongwei Shen 《Mathematische Annalen》2006,336(3):697-725
We study the homogeneous elliptic systems of order $2\ellWe study the homogeneous elliptic systems of order with real constant coefficients on Lipschitz domains in, . For any fixed p > 2, we show that a reverse H?lder condition with exponent p is necessary and sufficient for the solvability of the Dirichlet problem with boundary data in L
p
. We also obtain a simple sufficient condition. As a consequence, we establish the solvability of the L
p
Dirichlet problem for and . The range of p is known to be sharp if and . For the polyharmonic equation, the sharp range of p is also found in the case n = 6, 7 if , and if .Research supported in part by the NSF. 相似文献