Existence and regularity of minima for integral functionals noncoercive in the energy space
We show that local minimizers of functionals of the form , , are locally Lipschitz continuous provided f is a convex function with growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.
A simple dynamical problem involving unilateral contact and dry friction of Coulomb type is considered as an archetype. We are concerned with the existence and uniqueness of solutions of the system with Cauchy data. In the frictionless case, it is known [Schatzman, Nonlinear Anal. Theory, Methods Appl. 2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class . However, uniqueness is recovered provided that the data are analytic [Ballard, Arch. Rational Mech....
A simple dynamical problem involving unilateral contact and dry friction of Coulomb type is considered as an archetype. We are concerned with the existence and uniqueness of solutions of the system with Cauchy data. In the frictionless case, it is known [Schatzman, Nonlinear Anal. Theory, Methods Appl.2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class C∞. However, uniqueness is recovered provided that the data are analytic [Ballard, Arch. Rational...
This study deals with the existence and uniqueness of solutions to dynamical problems of finite freedom involving unilateral contact and Coulomb friction. In the frictionless case, it has been established [P. Ballard, Arch. Rational Mech. Anal. 154 (2000) 199–274] that the existence and uniqueness of a solution to the Cauchy problem can be proved under the assumption that the data are analytic, but not if they are assumed to be only of class C∞. Some years ago, this finding was extended [P. Ballard...
In this article, we want to show that it is possible to give a complete theory about the existence of an optimal control, without introducing any functional space, by means of the Non Standard Analysis.