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1.
Graziano Crasta 《Mathematische Zeitschrift》2000,235(3):569-589
We are concerned with the problem of existence, uniqueness and qualitative properties of solutions to the radially symmetric
variational problem
where is the ball of centered at the origin and with radius , the map is a normal integrand, and is a convex function of the second variable. This kind of problems, with non-convex lagrangians with respect to , arise in various fields of applied sciences, such as optimal design and nonlinear elasticity.
Received June 18, 1998; in final form August 26, 1999 / Published online September 14, 2000 相似文献
2.
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
3.
Summary. In this paper, we present a convergence analysis applicable to the approximation of a large class of semi-coercive variational
inequalities. The approach we propose is based on a recession analysis of some regularized Galerkin schema. Finite-element
approximations of semi-coercive unilateral problems in mechanics are discussed. In particular, a Signorini-Fichera unilateral
contact model and some obstacle problem with frictions are studied. The theoretical conditions proved are in good agreement
with the numerical ones.
Received January 14, 1999 / Revised version received June 24, 1999 / Published online July 12, 2000 相似文献
4.
We obtain some point-based sufficient conditions for the metric regularity in Robinson’s sense of implicit multifunctions in a finite-dimensional setting. The new implicit function theorem (which is very different from the preceding results of Ledyaev and Zhu [Yu.S. Ledyaev, Q.J. Zhu, Implicit multifunctions theorems, Set-Valued Anal. 7 (1999) 209–238], Ngai and Théra [H.V. Ngai, M. Théra, Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization, Set-Valued Anal. 12 (2004) 195–223], Lee, Tam and Yen [G.M. Lee, N.N. Tam, N.D. Yen, Normal coderivative for multifunctions and implicit function theorems, J. Math. Anal. Appl. 338 (2008) 11–22]) can be used for analyzing parametric constraint systems as well as parametric variational systems. Our main tools are the concept of normal coderivative due to Mordukhovich and the corresponding theory of generalized differentiation. 相似文献
5.
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
6.
N.H. Chieu 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(1):154-160
In this paper we show that the positive semi-definiteness (PSD) of the Fréchet and/or Mordukhovich second-order subdifferentials can recognize the convexity of C1 functions. However, the PSD is insufficient for ensuring the convexity of a locally Lipschitz function in general. A complete characterization of strong convexity via the second-order subdifferentials is also given. 相似文献
7.
We prove a theorem for the existence of solutions to a variational problem, under assumptions that do not require the convexity of the integrand. 相似文献
8.
For a family of nonlocal variational problems, a relaxation in terms of Young measures associated with minimizing sequences
is discussed and explicitly computed. The nonlocality character is the main new feature. These computations generalize the
same sort of ideas previously used in the analysis of micromagnetics to the case of magnetostriction in which interactions
between elastic and magnetic properties are considered. This situation, however, is analyzed under important simplifying assumptions
in dimension two.
Received June 25, 1998 / Accepted February 26, 1999 相似文献
9.
In this paper we report new results on the regularity of optimal controls for dynamic optimization problems with functional inequality state constraints, a convex time-dependent control constraint and a coercive cost function. Recently, it has been shown that the linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition, that requires linear independence merely with respect to non-negative weighting parameters, provided the control constraint set is independent of the time variable. We show that, if the control constraint set, regarded as a time-dependent multifunction, is merely Lipschitz continuous with respect to the time variable, then optimal controls can fail to be Lipschitz continuous. In these circumstances, however, a weaker Hölder continuity-like regularity property can be established. On the other hand, Lipschitz continuity of optimal controls is guaranteed for time-varying control sets under a positive linear independence hypothesis, when the control constraint sets are described, at each time, by a finite collection of functional inequalities. 相似文献
10.
Nguyen Dong Yen 《Set-Valued Analysis》1995,3(1):1-10
We obtain some characteristic properties of a subclass of multifunctions introduced by B. Ricceri and give a new proof for the result of P. Cubiotti on the existence of solutions to generalized quasi-variational inequalities involving multifunctions from the class. 相似文献
11.
A. B. Levy 《Set-Valued Analysis》1993,1(4):379-392
Epi-derivatives have many applications in optimization as approached through nonsmooth analysis. In particular, second-order epi-derivatives can be used to obtain optimality conditions and carry out sensitivity analysis. Therefore the existence of second-order epi-derivatives for various classes of functions is a topic of considerable interest. A broad class of composite functions on
n
called fully amenable functions (which include general penalty functions composed withC
2 mappings, possibly under a constraint qualification) are now known to be twice epi-differentiable. Integral functionals appear widely in problems in infinite-dimensional optimization, yet to date, only integral functionals defined by convex integrands have been shown to be twice epi-differentiable, provided that the integrands are twice epi-differentiable. Here it is shown that integral functionals are twice epi-differentiable even without convexity, provided only that their defining integrands are twice epi-differentiable and satisfy a uniform lower boundedness condition. In particular, integral functionals defined by fully amenable integrands are twice epi-differentiable under mild conditions on the behavior of the integrands.This work was supported in part by the National Science Foundation under grant DMS-9200303. 相似文献
12.
Pietro Celada Stefania Perrotta 《Calculus of Variations and Partial Differential Equations》2001,12(4):371-398
We consider the problem of minimizing multiple integrals of product type, i.e.
where is a bounded, open set in , is a possibly nonconvex, lower semicontinuous function with p-growth at infinity for some and the boundary datum is in (or simply in if ). Assuming that the convex envelope off is affine on each connected component of the set , we prove attainment for () for every continuous, positively bounded below function g such that (i) every point is squeezed between two intervals where g is monotone and (ii) g has no strict local minima. This shows in particular that the class of coefficents g that yield existence to () is dense in the space of continuous, positive functions on . We present examples which show that these conditions for attainment are essentially sharp.
Received April 12, 2000 / Accepted May 9, 2000 / Published online November 9, 2000 相似文献
13.
J. Chabrowski 《Calculus of Variations and Partial Differential Equations》1995,3(4):493-512
We formulate the concentration-compactness principle at infinity for both subcritical and critical case. We show some applications to the existence theory of semilinear elliptic equations involving critical and subcritical Sobolev exponents. 相似文献
14.
Luigi Ambrosio Nicola Fusco John E. Hutchinson 《Calculus of Variations and Partial Differential Equations》2003,16(2):187-215
The paper is concerned with the higher regularity properties of the minimizers of the Mumford–Shah functional. It is shown
that, near to singular points where the scaled Dirichlet integral tends to 0, the discontinuity set is close to an Almgren
area minimizing set. As a byproduct, the set of singular points of this type has Hausdorff dimension at most N-2, N being the dimension of the ambient space. Assuming higher integrability of the gradient this leads to an optimal estimate
of the Hausdorff dimension of the full singular set.
Received: 5 July 2001 / Accepted: 29 November 2001 / Published online: 23 May 2002 相似文献
15.
I. Fonseca G. Leoni R. Paroni 《Calculus of Variations and Partial Differential Equations》2003,17(3):283-309
It is proved that if , with p > 1, if is bounded in , , and if in then provided is 2-quasiconvex and satisfies some appropriate growth and continuity condition. Characterizations of the 2-quasiconvex envelope
when admissible test functions belong to BHp are provided.
Received: 10 October 2001 / Accepted: 8 May 2002 / Published online: 17 December 2002 相似文献
16.
Giulia Treu Mihai Vornicescu 《Calculus of Variations and Partial Differential Equations》2000,11(3):307-319
We consider the following problems
where is a convex function, is an open bounded subset of is a closed convex subset of such that and and are suitable obstacles. We give conditions on the function {\it g} under which the two problems are equivalent.
Received March 24, 1999/ Accepted January 14, 2000 / Published online June 28, 2000 相似文献
17.
Neil S. Trudinger Xu-Jia Wang 《Calculus of Variations and Partial Differential Equations》2001,13(1):19-31
The Monge mass transfer problem, as proposed by Monge in 1781, is to move points from one mass distribution to another so
that a cost functional is minimized among all measure preserving maps. The existence of an optimal mapping was proved by Sudakov
in 1979, using probability theory. A proof based on partial differential equations was recently found by Evans and Gangbo.
In this paper we give a more elementary and shorter proof by constructing an optimal mapping directly from the potential functions
of Monge and Kantorovich.
Received May 23, 2000 / Accepted June 12, 2000 / Published online November 9, 2000 相似文献
18.
《Optimization》2012,61(4-5):541-554
A new minimax approach for treating semicoercive hemivariational inequalities is presented. An elliptic Dirichlet problem at resonance and with discontinuous nonlinearties is solved under a recession condition 相似文献
19.
Lionel Thibault 《Journal of Differential Equations》2003,193(1):1-26
Differential inclusions involving the normal cone to a moving set are investigated. A special attention is paid to the sweeping process associated with sets for which no regularity assumption is required. 相似文献
20.
Non-local approximation of the Mumford-Shah functional 总被引:3,自引:0,他引:3
The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of -convergence by a sequence of non-local integral functionals.
Received June 6, 1996 / Accepted July 11, 1996 相似文献