We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals of the form

The paper studies the solution stability of a parametric control problem governed by semilinear elliptic equations with mixed state-control constraint, where objective function is nonconvex and admissible set unbounded. We show that under certain conditions, upper semicontinuous continuous respect to parameters.

In this note we show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semi-continuity of algebraic dimensions in any sense does not hold in general for families of compact non-Kähler manifolds. In the Kähler case, the upper semi-continuity always hol...

In this paper, we consider a discrete delay problem with negative feedback _ x(t) = f(x(t); x(t?1)) along with a certain family of time discretizations with stepsize 1=n. In the original problem, the attractor admits a Morse decomposition. We proved in G,H] that the discretized problems have global attractors. It was proved in G,M] that such attractors also admit Morse decompositions. In G,H] w...

* Correspondence: jeky99@126. com; [email protected] School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract In this article, we consider a class of parametric generalized vector quas...

Many tasks in image processing can be tackled by modeling an appropriate data fidelity term $\Phi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}$ and then solve one of the regularized minimization problems \begin{align*}&{}(P_{1,\tau}) \qquad \mathop{\rm argmin}_{x \in \mathbb R^n} \big\{ \Phi(x) \;{\rm s.t.}\; \Psi(x) \leq \tau \big\} \\&{}(P_{2,\lambda}) \qquad \mathop{\rm argmin}_{x \...

In two recent papers, Facchinei 7] and Facchinei and Kanzow 8] have shown that for a continuously diierentiable P 0-function f , the nonlinear complementarity problem NCP(f ") corresponding to the regularization f " (x) := f (x) + "x has a unique solution for every " > 0, that dist (x("); SOL(f)) ! 0 as " ! 0 when the solution set SOL(f) of NCP(f) is nonempty and bounded, and NCP(f) is stable i...

A rather general semilinear parabolic problem is studied together with its spatially semidiscrete nite element approximation. Both problems are formulated within the framework of nonlinear semigroups in the Sobolev space H 1 ((). The main result is an error estimate for solutions with initial data in H 1 ((), valid during an arbitrary nite time interval. The proof is based on the semigroup form...