共查询到20条相似文献,搜索用时 62 毫秒
1.
M. Flucher A. Garroni S. Müller 《Calculus of Variations and Partial Differential Equations》2002,14(4):483-516
We study the variational problem
where , is a bounded domain, , F satisfies $0\leq F|t|\leq \alpha |t|^{2^*}$ and is upper semicontinuous. We show that to second order in the value only depends on two ingredients. The geometry of enters through the Robin function (the regular part of the Green's function) and F enters through a quantity which is computed from (radial) maximizers of the problem in . The asymptotic expansion becomes
Using this we deduce that a subsequence of (almost) maximizers of must concentrate at a harmonic center of : i.e., , where is a minimum point of .
Received: 24 January 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001 相似文献
2.
Let F be a non-Archimedean local field and an integer. Let be irreducible supercuspidal representations of GL with . One knows that there exists an irreducible supercuspidal representation of GL, with , such that the local constants (in the sense of Jacquet, Piatetskii-Shapiro and Shalika) are distinct. In this paper, we show that, when is an unramified twist of , one may here takem dividingn and , for a prime divisor ofn depending on and the order of : in particular, , where is the least prime divisor of . This follows from a result giving control of certain divisibility properties of the conductor of a pair of supercuspidal
representations.
Received: 11 November 2000 / Accepted: 15 January 2001 / Published online: 23 July 2001 相似文献
3.
Shin-ichi Kobayashi 《Mathematische Annalen》2002,323(3):609-623
Let E be an elliptic curve over a number field F. The root number is conjecturally the sign of the functional equation of L-function of E/F. It is defined as the product of local signs over all places of F. The purpose of this paper is to describe this local sign by the coefficients of a Weierstra? equation of E.
Received: 31 March 2000 / Revised version: 22 November 2001 / Published online: 23 May 2002 相似文献
4.
Giuseppina Vannella 《Annali di Matematica Pura ed Applicata》2002,180(4):429-440
We consider a Neumann problem of the type -εΔu+F
′(u(x))=0 in an open bounded subset Ω of R
n
, where F is a real function which has exactly k maximum points.
Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.
Received: October 30, 1999 Published online: December 19, 2001 相似文献
5.
Daisuke Matsushita 《Mathematische Annalen》2001,321(4):755-773
We classify singular fibres over general points of the discriminant locus of projective Lagrangian fibrations over 4-dimensional
holomorphic symplectic manifolds. The singular fibre F is the following either one: F is isomorphic to the product of an elliptic curve and a Kodaira singular fibre up to finite unramified covering or F is a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is
Dynkin diagram of type or . Moreover, we show all types of the above singular fibres actually occur.
Received: 10 March 2000 / Revised version: 29 September 2000 / Published online: 24 September 2001 相似文献
6.
Simone Costa 《组合设计杂志》2020,28(5):366-383
Let F be a 2‐regular graph of order v. The Oberwolfach problem, OP(F), asks for a 2‐factorization of the complete graph on v vertices in which each 2‐factor is isomorphic to F. In this paper, we give a complete solution to the Oberwolfach problem over infinite complete graphs, proving the existence of solutions that are regular under the action of a given involution free group G. We will also consider the same problem in the more general context of graphs F that are spanning subgraphs of an infinite complete graph and we provide a solution when F is locally finite. Moreover, we characterize the infinite subgraphs L of F such that there exists a solution to OP(F) containing a solution to OP(L). 相似文献
7.
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
8.
Note on the spectrum of the Hodge-Laplacian for k-forms on minimal Legendre submanifolds in S^{2n+1}
Knut Smoczyk 《Calculus of Variations and Partial Differential Equations》2002,14(1):107-113
Given a minimal Legendre immersion L in and we prove that is an eigenvalue of the Hodge-Laplacian acting on k and (k-1)-forms on L. In particular we show that the eigenspaces Eig and Eig are at least of dimension
Received: 10 February 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001 相似文献
9.
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
10.
Henry C. Wente 《Calculus of Variations and Partial Differential Equations》2002,14(2):193-211
We consider large solutions of annular type to the volume constrained Douglas problem. They are conformally immersed H-surfaces. By rescaling we set the volume functional at one while the boundary curves shrink to the origin. We show that the
solutions become spherical in a precise manner. Spherical bubbling may fail if the conformality condition is dropped. We also
discuss the rotationally symmetric annular solutions to the H-surface equation and consider some illustrative examples.
Received: 2 May 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001 相似文献
11.
Automorphism groups of Weyl-type algebras 总被引:2,自引:0,他引:2
Let F be a field of characteristic 0, be n commuting variables over F, and be the field of all rational functions. Let . We have the simple Weyl type algebra . In this paper, the automorphism group of the associative algebra and the automorphism group of the Lie algebra are determined,
and it is proved that .
Received: 4 October 2001 / Revised version: 5 November 2001 相似文献
12.
In this paper we discuss the global behaviour of some connected sets of solutions of a broad class of second order quasilinear elliptic equations
for where is a real parameter and the function u is required to satisfy the condition
The basic tool is the degree for proper Fredholm maps of index zero in the form due to Fitzpatrick, Pejsachowicz and Rabier.
To use this degree the problem must be expressed in the form where J is an interval, X and Y are Banach spaces and F is a map which is Fredholm and proper on closed bounded subsets. We use the usual spaces and . Then the main difficulty involves finding general conditions on and b which ensure the properness of F. Our approach to this is based on some recent work where, under the assumption that and b are asymptotically periodic in x as $\left| x\right| \rightarrow\infty$, we have obtained simple conditions which are necessary and sufficient for to be Fredholm and proper on closed bounded subsets of X. In particular, the nonexistence of nonzero solutions in X of the asymptotic problem plays a crucial role in this issue. Our results establish the bifurcation of global branches of
solutions for the general problem. Various special cases are also discussed. Even for semilinear equations of the form
our results cover situations outside the scope of other methods in the literature.
Received March 30, 1999; in final form January 17, 2000 / Published online February 5, 2001 相似文献
13.
14.
Ulrich Clarenz 《Calculus of Variations and Partial Differential Equations》2002,15(3):313-324
In the following paper we study parametric functionals. First we introduce a generalized mean curvature (so called F-mean curvature). This enables us to describe extremals of parametric funcionals as surfaces of prescribed F-mean curvature. Furthermore we give a differential equation for arbitrary immersions generalizing and apply this equation to surfaces of vanishing and prescribed F-mean curvature. Especially we prove non-existence results for such surfaces generalizing Theorems by Hildebrandt and Dierkes
[3], [6].
Received: 11 May 2001 / Accepted: 11 July 2001 / Published online: 12 October 2001 相似文献
15.
Let F be a finite field or an algebraic number field. In previous papers we have shown how to find the basic building blocks (the radical and the simple components) of a finite dimensional algebra over F in polynomial time (deterministically in characteristic zero and Las Vegas in the finite case). A finite-dimensional simple algebra A is a full matrix algebra over some not necessarily commutative extension field G of F. The problem remains to find G and an isomorphism between A and a matrix algebra over G. This, too, can be done in polynomial time for finite F. We indicate in the present paper that the problem for F = Q might be substantially more difficult. We link the problem to hard number theoretic problems such as quadratic residuosity modulo a composite number. We show that assuming the generalized Riemann hypothesis, there exists a randomized polynomial time reduction from quadratic residuosity to determining whether or not a given 4-dimensional algebra over Q has zero divisors. It will follow that finding a pair of zero divisors is at least as hard as factoring squarefree integers. 相似文献
16.
Bernard Dacorogna Irene Fonseca 《Calculus of Variations and Partial Differential Equations》2002,14(2):115-149
The study of existence of solutions of boundary-value problems for differential inclusions
where , is an open subset of , is a compact set, and B is a -valued first order differential operator, is undertaken. As an application, minima of the energy for large magnetic bodies
where the magnetization is taken with values on the unit sphere is the induced magnetic field satisfying and is the anisotropic energy density, and the applied external magnetic field is given by , are fully characterized. Setting with , it is shown that E admits a minimizer with if and only if either 0 is on a face of or , where denotes the convex hull of Z.
Received: 6 November 2000 / Accepted: 23 January 2001 / Published online: 23 April 2001 相似文献
17.
Michael Filippakis Leszek Gasiński Nikolaos S. Papageorgiou 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(1):43-66
We consider the periodic problem for differential inclusions in
$$ \user2{\mathbb{R}}^{\rm N} $$ with a nonconvex-valued orientor field F(t, ζ), which is lower semicontinuous in
$$ \zeta \in \user2{\mathbb{R}}^{\rm N} $$ Using the notion of a nonsmooth, locally Lipschitz generalized guiding function,
we prove that the inclusion has periodic solutions. We have two such existence theorems. We also study the “convex” periodic
problem and prove an existence result under upper semicontinuity hypothesis on F(t, ·) and using a nonsmooth guiding function. Our work was motivated by the recent paper of Mawhin-Ward [23] and extends the
single-valued results of Mawhin [19] and the multivalued results of De Blasi-Górniewicz-Pianigiani [4], where either the guiding
function is C1 or the conditions on F are more restrictive and more difficult to verify. 相似文献
18.
Consider a linear regression model, Y=β′X+ε where Y may be right censored and the cdf F
o of ε is unknown. We show that a modified semi-parametric MLE, denoted by is strongly consistent under certain regularity conditions. Moreover, if F
o is discontinuous, then P(≠β i.o.)=0, which means that P(=β if the sample size is large)=1. The latter property has not been reported for the existing estimators. By contrast, most
estimators, such as the Buckley-James estimator and M-estimators , satisfy that P(≠β i.o.)=1.
Received April 23, 2001, Accepted November 13, 2001 相似文献
19.
Ali Mouhib 《Mathematische Nachrichten》2019,292(3):633-639
Let r be a positive integer. Assume Greenberg's conjecture for some totally real number fields, we show that there exists an infinite family of imaginary cyclic number fields F over the field of rational number field , with an elementary 2‐class group of rank equal to r that capitulates in an unramified quadratic extension over F. Also, we give necessary and sufficient conditions for the Galois group of the unramified maximal 2‐extension over F to be abelian. 相似文献
20.
The first part of this paper establishes the existence of a minimizer of problem:
where
The essential features of the integrand are that
where We show that the minimizer satisfies an Euler- Lagrange equation and estimates are given for the Lagrange multiplier as a
function of d. In the second part of the paper, we use this result to establish the existence of guided TM-modes propagating through a
self-focusing anisotropic dielectric. These are special solutions of Maxwell's equations with a nonlinear constitutive relation
of a type commonly used in nonlinear optics when treating the propagation of waves in a cylindrical wave-guide. In TM-modes,
the magnetic field has the form
\[ {\bf B}=w(r)\cos (kz-\omega t)i_{\theta } \]
when expressed in cylindrical polar co-ordinates The amplitude w is given by where is a minimizer of the problem (0.1) for a function which is determined by the constitutive relation through a Legendre transformation.
Received: 4 April 2001 / Accepted: 29 November 2001 / Published online: 28 February 2002 相似文献