Lower Semicontinuity in SBH

The aim of this paper consists in giving a first characterization of lower semicontinuity for surface integrals in the space of special functions of bounded hessian, showing at the same time some conditions necessarily verified by the integrands. Partially supported by FCT/POCTI/FEDER.     

Semicontinuity and Quasiconvex Functions

Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.     

Semicontinuity of the spectrum at infinity

We prove that, for an analytic family of “weakly tame” regular functions on an affine manifold, the spectrum at infinity of each function of the family is semicontinuous in the sense of Varchenko.     

Many Valued Topologies and Lower Semicontinuity

On the basis of join-continuous semigroups , this paper demonstrates among other things that on every complete ortholattice there exists an L-valued topology such that order convergence is L-topological (this is not always the case with respect to ordinary topologies). Further, the concept of lower semicontinuous lattice-valued maps permits an extension of the omega-functor to the general setting of L-valued topological spaces where the importance of lies in the replacement of ordinary topologies by L-valued topologies. It is shown that has a right adjoint functor iff the underlying lattice is continuous.     

On the Semicontinuity of Curvature Integrals

Let H_j(K, ·) be the j – th elementary symmetric function of the principal curvatures of a convex body K in Euclidean d – space. We show that the functionals ∫_bd f(H_j(K, x)) dℋ︁^d—1(x) depend upper semicontinuously on K, if f : [0, ∞) is concave, lim_t→0f(t) = 0, and lim_t→∞f(t)/t = 0. An analogous statement holds for integrals of elementary symmetric functions of the principal radii of curvature.     

Lower Semicontinuity of a Non-Hyperbolic Attractor

The unstable invariant set near a non-hyperbolic stationarypoint of an abstract parabolic equation is studied. Lower semicontinuityof the attractor for the Chafee-Infante problem in the caseof the non-hyperbolic zero stationary solution is proved.     

Semicontinuity of a functional depending on curvature

In this paper we prove a lower semicontinuity result for a functional , defined on a class of bounded subsets of with a piecewise boundary, with respect to the -convergence of the sets. The functional depends on the curvature of in a linear way and contains a penalizing term which prevents the appearance of thin sets in the symmetric difference , where in an -approximating sequence of . Received: 3 January 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001     

变分泛函的半连续性问题

研究了非多项式增长的变分泛函,利用Orlicz空间理论,得到了其在Orlicz-Sobolev空间中弱序列下半连续的充要条件,推广了关于多项式增长的变分泛函的相应结论。     

Optimization and Stability Results Through Cone Lower Semicontinuity

We establish optimization results for set-valued mappings, with the image space given by a topological vector space partially ordered by a cone. Moreover, we obtain stability results relative to parametrized optimization problems. We use a weak semicontinuity concept related to the order structure of the image space and show how compactness assumptions used in previous papers can be lightened.     

Lower Semicontinuity and Upper Semicontinuity of the Solution Sets and Approximate Solution Sets of Parametric Multivalued Quasivariational Inequalities

We consider the semicontinuity of the solution set and the approximate solution set of parametric multivalued quasivariational inequalities in topological vector spaces. Three kinds of problems arising from the multivalued situation are investigated. A rather complete picture, which is symmetric for the two kinds of semicontinuity (lower and upper semicontinuity) and for the three kinds of multivalued quasivariational inequality problems, is supplied. Moreover, we use a simple technique to prove the results. The results obtained improve several known ones in the literature. This research was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. The final part of this work was completed during a stay of the first author at the Department of Mathematics, University of Pau, Pau, France, and its hospitality is acknowledged.     

Semicontinuity of the solution map of quasivariational inequalities

We investigate continuity properties (closedness and lower semicontinuity) of the solution map of a quasivariational inequality which is subjet to perturbations. Perturbations are here considered both on the set-valued operator and on the constraint map defining the quasivariational inequality. Two concepts of solution map will be considered.