On the Efficient Solution of Nonlinear Finite Element Equations I.
On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation
On the Equality of two Stieltjes Integrals in the Complex Plane
On the equivalence of variational problems. II
Elements of general theory of infinitely prolonged underdetermined systems of ordinary differential equations are outlined and applied to the equivalence of one-dimensional constrained variational integrals. The relevant infinite-dimensional variant of Cartan’s moving frame method expressed in quite elementary terms proves to be surprisingly efficient in solution of particular equivalence problems, however, most of the principal questions of the general theory remains unanswered. New concepts of...
On the equivalence of variational problems. III
On the ersatz material approximation in level-set methods
The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire et al., J. Comput. Phys.194 (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...
On the evaluation of finite element sensitivities to nodal coordinates.
On the existence and convergence of approximate solutions for equilibrium problems in Banach spaces.
On the existence of a solution for some distributed optimal control hyperbolic system.
On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs
The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space , on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space .
On the existence of area-minimizing surfaces with free boundary.
On the Existence of Integral Currents with Prescribed Mean Curvature Vector.
On the existence of optimal controls for nonlinear infinite dimensional systems
We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
On the existence of optimal processes
On the Existence of Optimal Solutions for Infinite Horizon Optimal Control Problems: Nonconvex and Multicriteria Problems
In questa Nota si continua la discussione iniziata in [4] dell'esistenza di soluzioni ottimali per problemi di ottimo controllo in . Si definiscono problemi generalizzati, e si ottengono estensioni di risultati già presentati in [4]. Si dimostrano anche varie relazioni tra le soluzioni ottimali dei problemi generalizzati e i problemi originali e non convessi di ottimo controllo. Alla fine si considerano problemi lineari nelle variabili di stato anche nel caso di costi funzionali a valori vettoriali...
On the existence of solutions to a problem in multidimensional segmentation
On the Existence of Surfaces with Prescribed Mean Curvature and Boundary.
On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
On the existence of the price equilibrium by different methods
We have given several proofs on the existence of the price equilibrium --- via variational inequality --- via degree theory and via Brouwer's theorems.
On the existence of variations, possibly with pointwise gradient constraints
We propose a necessary and sufficient condition about the existence of variations, i.e., of non trivial solutions to the differential inclusion .