共查询到20条相似文献,搜索用时 375 毫秒
1.
Nicola Visciglia 《Calculus of Variations and Partial Differential Equations》2005,24(2):167-184
We present a generalized version of the Hardy-Sobolev inequality, in which the homogeneous potential
is replaced by any potential V belonging to the Lorentz space
. We show that the best constant in these inequalities is achieved provided that
where
. We also analyze the limit case
. Finally an application to a non-linear eigenvalues problem with rough potentials is presented.Received: 19 September 2004, Accepted: 15 November 2004, Published online: 22 December 2004 相似文献
2.
Marina Ghisi Massimo Gobbino 《Calculus of Variations and Partial Differential Equations》2005,24(1):111-129
We study a variational problem arising from a generalization of an economic model introduced by Rochet and Choné in [5]. In this model a monopolist proposes a set Y of products with price list
. Each rational consumer chooses which product to buy by solving a personal minimum problem, taking into account his/her tastes and economic possibilities. The monopolist looks for the optimal price list which minimizes costs, hence maximizes the profit. This leads to a minimum problem for functionals
(the “pessimistic cost expectation”) and
(the “optimistic cost expectation”), which are in turn defined through two nested variational problems. We prove that the minimum of
exists and coincides with the infimum of
. We also provide a variational approximation of
by smooth functionals defined in finite dimensional Euclidean spaces.Received: 2 March 2004, Accepted: 19 October 2004, Published online: 22 December 2004Mathematics Subject Classification (2000):
49J45, 91B 相似文献
3.
Min-Chun Hong Changyou Wang 《Calculus of Variations and Partial Differential Equations》2005,23(4):425-450
For
and
, we show that any minimizing biharmonic map from
to Sk is smooth off a closed set whose Hausdorff dimension is at most n-5. When n = 5 and k = 4, for a parameter
we introduce a
-relaxed energy
of the Hessian energy for maps in
so that each minimizer
of
is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of
for
.Received: 5 April 2004, Accepted: 19 October 2004, Published online: 10 December 2004 相似文献
4.
Yavdat Il’yasov Thomas Runst 《Calculus of Variations and Partial Differential Equations》2005,22(1):101-127
This paper concerns with a family of inhomogeneous Neumann boundary value problems having indefinite nonlinearities which depend on a real parameter
. We discuss the existence and the multiplicity of positive solutions with respect to
. Developing the fibering method further, we can introduce a constructive concept of the calculation of certain nonlocal intervals
, the so-called sufficient intervals of the existence. Then we are able to prove some new results on the existence and the multiplicity of positive solutions
for
.Received: 22 December 2003, Accepted: 29 January 2004, Published online: 16 July 2004Mathematics Subject Classification (2000):
35J70, 35J65, 47H17 相似文献
5.
We consider the following singularly perturbed semilinear elliptic problem:
where
is a bounded domain in R
N
with smooth boundary
,
is a small constant and f is some superlinear but subcritical nonlinearity. Associated with (I) is the energy functional
defined by
where
. Ni and Takagi ([29, 30]) proved that for a single boundary spike solution
, the following asymptotic expansion holds:
where c
1 > 0 is a generic constant,
is the unique local maximum point of
and
is the boundary mean curvature function at
. In this paper, we obtain a higher-order expansion of
where c
2, c
3 are generic constants and
is the scalar curvature at
. In particular c
3 > 0. Some applications of this expansion are given.Received: 14 January 2003, Accepted: 28 July 2003, Published online: 15 October 2003Mathematics Subject Classification (2000):
Primary 35B40, 35B45; Secondary 35J25 相似文献
6.
We obtain necessary and sufficient conditions for the solvability of the augmentation and modification problems of order
for Hermitian matrices. The augmentation problem consists in the construction of a Hermitian
-matrix with a given
-block
in block
-representation and with the prescribed eigenvalues. The modification problem consists in the construction of a Hermitian
-matrix
of rank not greater than
so that the obtained matrix, being added to a given Hermitian
-matrix
, will have the required spectrum. We give an estimate for the minimal number of different eigenvalues of the solutions to these problems. 相似文献
7.
Ovidiu Savin 《Calculus of Variations and Partial Differential Equations》2005,22(3):303-320
We consider the following obstacle problem for Monge-Ampere equation
and discuss the regularity of the free boundary
. We prove that
is
if f is bounded away from 0 and
, and it is C
1,1 if
.Received: 4 February 2003, Accepted: 3 March 2004, Published online: 16 July 2004 相似文献
8.
Daniele Castorina Filomena Pacella 《Calculus of Variations and Partial Differential Equations》2005,23(2):125-138
We consider the subcritical problem
& 0 & \qquad\textrm{in} \; A\\
u & = & 0 & \qquad\textrm{on} \; \delta A\\
\end{array}
\right.$$" align="middle" border="0">
where A is an annulus in
,
,
is the critical Sobolev exponent and
0$" align="middle" border="0">
is a small parameter. We prove that solutions of (I) which concentrate at one or two points are axially symmetric.Received: 7 July 2003, Accepted: 10 May 2004, Published online: 16 July 2004Filomena Pacella: Research supported by MIUR, project Variational Methods and Nonlinear Differential Equations. 相似文献
9.
Marc Oliver Rieger Paolo Tilli 《Calculus of Variations and Partial Differential Equations》2005,23(4):373-390
We study by means of
-convergence the asymptotics of the rescaled Mumford-Shah functional
when
and prove the existence of a
-limit. The limit functional is easy to handle and can be used as a simple approximation to the original Mumford-Shah functional. Moreover, its minimizers can be interpreted as a sort of asymptotic probability distribution of the sets
. Some examples illustrate the use of this method in image segmentation.Received: 12 June 2004, Accepted: 12 July 2004, Published online: 10 December 2004 相似文献
10.
The solutions of the equation
in
, where
are investigated,
Bessel potentials of higher order are defined, and recurrence relations
between these solutions and these Bessel potentials are obtained. It is
also proved that these solutions and the solutions of
, under certain conditions, are identical.
Received: 6 November 2002 相似文献
11.
Mariano Giaquinta Domenico Mucci 《Calculus of Variations and Partial Differential Equations》2005,24(2):155-166
Let
be a smooth 1-connected compact oriented manifold without boundary, such that its 2-homology group has no torsion. We characterize in any dimension n the weak
lower semicontinuous envelope of the Dirichlet integral of Sobolev maps in
.Received: 6 November 2004, Accepted: 15 November 2004, Published online: 22 December 2004 相似文献
12.
Donatella Danielli Arshak Petrosyan 《Calculus of Variations and Partial Differential Equations》2005,23(1):97-124
In this paper we prove
regularity (near flat points) of the free boundary
0\}\cap\Omega$" align="middle" border="0">
in the Alt-Caffarelli type minimum problem for the p-Laplace operator:
0\}}\right)dx\rightarrow \min\qquad
(1
Received: 3 June 2003, Accepted: 9 June 2004, Published online: 8 February 2005Mathematics Subject Classification (2000): 35R35, 35J60The first author is partially supported by NSF Grant DMS-0202801 and NSF CAREER Grant DMS-0239771 相似文献
13.
Given an almost complex structure J in a cylinder of
(p > 1) together with a compatible symplectic form
and given an arbitrary J-holomorphic curve
without boundary in that cylinder, we construct an holomorphic perturbation of
, for the canonical complex structure J
0 of
, such that the distance between these two curves in W
1,2 and
norms, in a sub-cylinder, are controled by quantities depending on J,
and by the area of
only. These estimates depend neither on the topology nor on the conformal class of
. They are key tools in the recent proof of the regularity of 1-1 integral currents in [RT].Received: 2 October 2003, Accepted: 18 November 2003, Published online: 25 February 2004 相似文献
14.
Let
and
be Hausdorff topological vector spaces over the field
, let
be a bilinear functional, and let
be a non-empty subset of
. Given a set-valued map
and two set-valued maps
, the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point
and a point
such that
and
for all
and for all
or to find a point
a point
and a point
such that
and
for all
. The generalized bi-quasi-variational inequality was introduced first by Shih and Tan [8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators [4] in locally convex topological vector spaces on compact sets. 相似文献
15.
We study the regularizing effect of perimeter penalties for a problem of optimal compliance in two dimensions. In particular, we consider minimizers of
where
The sets
,
, and the force f are given. We show that if we consider only scalar valued u and constant
, or if we consider the elastic energy
, then
is
away from where
is pinned. In the scalar case, we also show that, for any
of class
,
is
. The proofs rely on a notion of weak outward curvature of
, which we can bound without considering properties of the minimizing fields, together with a bootstrap argument.Received: 5 March 2002, Accepted: 3 September 2002, Published online: 17 December 2002 相似文献
16.
Let G be a finite group,
a normal subgroup, p a prime,
a finite splitting field of characteristic p for
G and
We prove that
is a splitting field for N, using the action
of the Galois group of the field extension
on the irreducible representations of N.
As
is a splitting field for the symmetric group
Sn
we get as a corollary that
is a splitting field for the alternating group
An.
Received: 31 July 2003 相似文献
17.
G. V. Kuz'mina 《Journal of Mathematical Sciences》2003,118(1):4880-4894
We apply a variant of the method of the extremal metric to some problems concerning extremal decompositions and related problems. Let
be a system of distinct points on
and let
be the family of all systems
of nonoverlapping simply connected domains on
such that
. Let
where
is the reduced module of the domain
with respect to the point
. At present, the problem concerning the value
was solved completely for
. In this work, we continue the previous author's investigations and consider the case
. In addition, we consider the problem concerning the maximum of the sum
in the family
introduced above, where
, are arbitrary points of the circle
, and is a positive number. We prove that if
, then the maximum is attained only for systems of equidistant points of the circle
. For
, this result was obtained earlier by Dubinin who applied the method of symmetrization. It is shown that if
, where
is an even number, then equidistant points of the circle
do not realize the indicated maximum. Bibliography: 11 titles. 相似文献
18.
Helena Ferreira 《Extremes》2000,3(4):385-392
Let
be a sequence of identically distributed variables. We study the asymptotic distribution of
, where Y
[r:n] denotes the concomitant of the rth order statistic X
r:n
, corresponding to
, and
is held fixed while
. Conditions are given for the
and
to have the same asymptotic behavior as that we would apply if
were i.i.d. The result is illustrated with a simple linear regression model
, where
is a stationary sequence with extremal index
. 相似文献
19.
We present a characterization of ideal knots, i.e., of closed knotted curves of prescribed thickness with minimal length, where we use the notion of global curvature for the definition of thickness. We show with variational methods that for an ideal knot
, the normal vector
at a curve point
is given by the integral over all vectors
against a Radon measure, where
realizes the given thickness. As geometric consequences we obtain in particular, that points without contact lie on straight segments of
, and for points
with exactly one contact point
we have that
points exactly into the direction of
Moreover, isolated contact points lie on straight segments of
, and curved arcs of
consist of contact points only, all realizing the prescribed thickness with constant (maximal) global curvature.Received: 1 January 2003, Accepted: 12 March 2003, Published online: 1 July 2003Mathematics Subject Classification (2000):
53A04, 57M25, 74K05, 74M15, 92C40 相似文献
20.
For each
, we solve the following variational problem
and we show that
.Received: 4 November 2003, Accepted: 10 May 2004, Published online: 16 July 2004Radu Ignat: Radu.Ignat@ens.fr 相似文献