On minimal surfaces with free boundaries in given homotopy classes
We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. The functionals considered belong to a class which includes semi-coercive, compact-coercive and P-coercive functionals. Some applications to nonlinear partial differential equations are given.
We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...
In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints , where is a closed set and is a set-valued map. No convexity requirements are imposed on . The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.
Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for...
Studiamo un problema ellittico quasilineare concernente un dominio circondato da un rinforzo sottile di spessore variabile, in cui il coefficiente dell'equazione è (localmente) non costante. Esso concerne due diversi esponenti, uno nel dominio e l'altro nel rinforzo, una condizione di Dirichlelet sulla frontiera esterna e una condizione di trasmissione. Prediciamo il comportamento asintotico della soluzione quando lo spessore, insieme con il coefficiente nel rinforzo, tende a zero perché essi siano...
We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.
We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a -Laplacian system. We prove...