共查询到20条相似文献,搜索用时 576 毫秒
1.
Martin Fuchs Gregory Seregin 《Calculus of Variations and Partial Differential Equations》1998,6(2):171-187
In the present paper we study regularity for local minimizers of the convex variational integral defined on certain classes of vector–valued functions . The underlying energy spaces are natural from the point of view of existence theory. We then show that local minimizers
are of class apart from a closed singular set with vanishing Lebesgue measure, provided . For twodimensional problems we obtain smoothness in the interior of .
Received June 21, 1996 / In revised form December 2, 1996 / Accepted December 17, 1996 相似文献
2.
Ivan Ginchev Juan-Enrique Martínez-Legaz 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6781-6787
A characterization of d.c. functions f:Ω→R in terms of the quasidifferentials of f is obtained, where Ω is an open convex set in a real Banach space. Recall that f is called d.c. (difference of convex) if it can be represented as a difference of two finite convex functions. The relation of the obtained results with known characterizations is discussed, specifically the ones from [R. Ellaia, A. Hassouni, Characterization of nonsmooth functions through their generalized gradients, Optimization 22 (1991), 401-416] in the finite-dimensional case and [A. Elhilali Alaoui, Caractérisation des fonctions DC, Ann. Sci. Math. Québec 20 (1996), 1-13] in the case of a Banach space. 相似文献
3.
We consider the variational inequality describing the stationary flow of a Bingham type fluid in bounded domains. Differentiability
properties of weak solutions in suitable energy spaces providing existence theorems are studied. We suppose that the volume
forces belong to classes of Morrey type and generalize our previous regularity results concerning slow, steady–state flow
of Bingham fluids.
Received: 12 February 1996; in final form 16 July 1996 相似文献
4.
In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet
boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence
theorem for minimax solutions and develop effective penalized procedures to approximate state constraints. Based on a careful
variational analysis, we establish convergence results and optimality conditions for approximating problems that allow us
to characterize suboptimal solutions to the original minimax problem with hard constraints. Then passing to the limit in approximations,
we prove necessary optimality conditions for the minimax problem considered under proper constraint qualification conditions.
Accepted 7 June 1996 相似文献
5.
Harmonic maps with potential 总被引:8,自引:0,他引:8
Ali Fardoun Andrea Ratto 《Calculus of Variations and Partial Differential Equations》1997,5(2):183-197
Let (M,g) and (N,h) be two Riemannian manifolds, and G:N →ℝ a given function. If f:M → N is a smooth map, we set E
G
(f)=12 ∫M [∣df∣2− 2G(f)]dv
g. We establish some variational properties and some existence results for the functional E
G
(f): in particular, we analyse the case of maps into a sphere.
Received April 29, 1996 / Accepted May 28, 1996 相似文献
6.
Hypercyclic subspaces of a Banach space 总被引:1,自引:0,他引:1
Recently a lot of research has been done on hypercyclicity of a bounded linear operator on a Banach space, based on the hypercyclicity criterion obtained by Kitai in 1982, and independently by Gethner and Shapiro in 1987. By combining this criterion with one extra condition, Montes-Rodríguez obtained in 1996 a sufficient condition for the operator to have a closed infinite dimensional hypercyclic subspace, with a very technical proof. Since then, this result has been used extensively to generate new results on hypercyclic subspaces. In the present paper, we give a simple proof of the result of Montes-Rodríguez, by first establishing a few elementary results about the algebra of operators on a Banach space. 相似文献
7.
Samuel Amstutz 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1585-1595
This paper deals with elliptic optimal control problems for which the control function is constrained to assume values in {0, 1}. Based on an appropriate formulation of the optimality system, a semismooth Newton method is proposed for the solution. Convergence results are proved, and some numerical tests illustrate the efficiency of the method. 相似文献
8.
Nguyen Thanh Qui 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1676-1689
Under a mild regularity assumption, we derive an exact formula for the Fréchet coderivative and some estimates for the Mordukhovich coderivative of the normal cone mappings of perturbed polyhedra in reflexive Banach spaces. Our focus point is a positive linear independence condition, which is a relaxed form of the linear independence condition employed recently by Henrion et al. (2010) [1], and Nam (2010) [3]. The formulae obtained allow us to get new results on solution stability of affine variational inequalities under linear perturbations. Thus, our paper develops some aspects of the work of Henrion et al. (2010) [1] Nam (2010) [3] Qui (in press) [12] and Yao and Yen (2009) [6] and [7]. 相似文献
9.
An optimal design problem with perimeter penalization 总被引:11,自引:0,他引:11
Luigi Ambrosio Giuseppe Buttazzo 《Calculus of Variations and Partial Differential Equations》1993,1(1):55-69
We study the optimal design problem of finding the minimal energy configuration for a mixture of two conducting materials when a perimeter penalization of the unknown domain is added. We show that in this situation an optimal domain exists and that, under suitable assumptions on the data, it is an open set.This work is part of the project EURHomogenization, contract SC1-CT91-0732 of the program SCIENCE of the Commission of the European Communities. 相似文献
10.
We consider the identification problem of two operators having different properties for the systems governed by nonlinear evolution equations. For the identification problem, we show the existence of optimal solutions and present necessary optimality conditions. We illustrate the approach on two examples. 相似文献
11.
Guido Cortesani 《Annali dell'Universita di Ferrara》1997,43(1):27-49
Let Ω be an open and bounded subset ofR
n
with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R
m
) whose jump setS
vis essentially closed and polyhedral and which are of classW
k, ∞ (S
v,R
m) for every integerk are strongly dense inGSBV
p(Ω,R
m
), in the sense that every functionu inGSBV
p(Ω,R
m
) is approximated inL
p(Ω,R
m
) by a sequence of functions {v
k{j∈N with the described regularity such that the approximate gradients ∇v
jconverge inL
p(Ω,R
nm
) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS
v
j converges to the (n−1)-dimensional measure ofS
u. The structure ofS
v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneu∈GSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.相似文献
12.
The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions.
In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation
solutions.
Accepted 27 February 1996 相似文献
13.
In this paper we give verifiable conditions in terms of limiting Fréchet subdifferentials ensuring the metric regularity of a multivalued functionF(x)=–g(x)+D. We apply our results to the study of the limiting Fréchet subdifferential of a composite function defined on a Banach space. 相似文献
14.
In this work we study the existence and asymptotic behavior of overtaking optimal trajectories for linear control systems
with convex integrands. We extend the results obtained by Artstein and Leizarowitz for tracking periodic problems with quadratic
integrands [2] and establish the existence and uniqueness of optimal trajectories on an infinite horizon. The asymptotic dynamics
of finite time optimizers is examined.
Accepted 31 January 1996 相似文献
15.
Generalized Semicontinuity and Existence Theorems for Cone Saddle Points 总被引:11,自引:0,他引:11
This paper is concerned with existence theorems for generalized saddle points (cone saddle points) of vector-valued functions.
A concept of lower semicontinuity for vector-valued functions is introduced and its properties are investigated. Previous
results of the author are extended by using the lower semicontinuity.
Accepted 26 April 1996 相似文献
16.
Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal control problem. We provide in this paper a general version of a turnpike theorem, valuable for nonlinear dynamics without any specific assumption, and for very general terminal conditions. Not only the optimal trajectory is shown to remain exponentially close to a steady-state, but also the corresponding adjoint vector of the Pontryagin maximum principle. The exponential closedness is quantified with the use of appropriate normal forms of Riccati equations. We show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method, or a shooting method. In particular, we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector, not at the initial time, but at the middle of the trajectory. 相似文献
17.
We present second-order subdifferentials of Clarke's type of C
1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in
n
, considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C
1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994. 相似文献
18.
Michele Carriero Antonio Leaci Franco Tomarelli 《Calculus of Variations and Partial Differential Equations》2008,32(1):81-110
We derive many necessary conditions for minimizers of a functional depending on free discontinuities, free gradient discontinuities
and second derivatives, which is related to image segmentation. 相似文献
19.
Peter Smith 《Acta Appl Math》1986,6(3):293-308
The usual notion of a saddle functional in the calculus of variations assumes a vex/concave structure over the product space
of two inner product spaces. Here the ideas extended to include some convexity in both spaces whilst still retaining an overall
saddle property. Dual extremum principles are established for these functionals. Examples include periodic solutions of Duffing's
equation, an iterative scheme and a pair of simultaneous partial differential equations which arise in magnetohydrodynamics. 相似文献
20.
Robert Deville 《Set-Valued Analysis》1994,2(1-2):141-157
We investigate various notions of subdifferentials and superdifferentials of nonconvex functions in Banach spaces. We prove stability results of these subdifferentials and superdifferentials under various kind of convergences. Our proofs rely on a recent variational principle of Deville, Godefroy and Zizler. Connections between our results, the geometry of Banach spaces and existence theorems of viscosity solutions for first and second-order Hamilton-Jacobi equations in infinite-dimensional Banach spaces will be explained. 相似文献