Existence Results for Noncoercive Variational Problems (original) (raw)

An existence result for a nonconvex variational problem via regularity

ESAIM: Control, Optimisation and Calculus of Variations, 2002

Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.

Some Results on Non-Coercive Variational Problems and Applications

Zeitschrift für Analysis und ihre Anwendungen, 1995

We give a necessary and sufficient condition to ensure the existence of solutions of three problems of the calculus of variations with non-coercive integrands. The solutions u we consider are lipschitz functions, i.e. tz E W"-(O, 1). The three problems depends on the same functionals but are different in the constraints. We consider respectively a problem without constraint, a problem with v' 0 and finally a problem with u 0. These problems can be related to optimal foraging models in behavioural ecology.

Existence theorems for nonconvex variational inequalities problems

Applied Mathematical Sciences, 2013

In this paper, we prove the existence theorem for a mapping defined by T = T 1 + T 2 when T 1 is a μ 1-Lipschitz continuous and γ-strongly monotone mapping, T 2 is a μ 2-Lipschitz continuous mapping, we have a mapping T is Lipschitz continuous but not strongly monotone mapping. This work is extend and improve the result of N. Petrot [17].

A remark on Gwinner's existence theorem on variational inequality problem

International Journal of Mathematics and Mathematical Sciences, 2000

Gwinner (1981) proved an existence theorem for a variational inequality problem involving an upper semicontinuous multifunction with compact convex values. The aim of this paper is to solve this problem for a multifunction with open inverse values.