The planar motion with bounded derivative of the curvature and its suboptimal paths.
The Plateau Problem for Surfaces of Prescribed Mean Curvature in a Cylinder.
The Plateau-Douglas problem for nonorientable minimal surfaces.
The plenary hull of the generalized Jacobian matrix and the inverse function theorem in subdifferential calculus
The principle of stationary action in the calculus of variations
We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Our main intention in this regard is to expose precise mathematical conditions for critical paths to be minimum solutions in a variety of situations of interest in Physics. Our claim is that, with a few elementary techniques, a systematic analysis (including the domain for which critical points are genuine minima) of non-trivial models...
The problem of the body of revolution of minimal resistance
Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of convex axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class of axially symmetric but generally nonconvex bodies. The infimum in this problem is not attained. We construct a sequence of bodies minimizing the resistance. This sequence approximates a convex body with smooth front surface, while the surface of approximating bodies...
The problem of the number of switches in parabolic equations with control
The quadratic control for linear discrete-time systems with independent random perturbations in Hilbert spaces connected with uniform observability.
The quadratic criterion of control process quality using the exponential weighting function
The Rayleigh quotient and dynamic programming.
The regularity of the trace for minimal surfaces
The Regularization of the Second Order Lagrangians in Example
This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.
The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity
The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.
The relaxed energy for -valued maps and measurable weights
The second order optimality conditions for nonlinear mathematical programming with data
To find nonlinear minimization problems are considered and standard -regularity assumptions on the criterion function and constrained functions are reduced to -regularity. With the aid of the generalized second order directional derivative for real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.
The second-order methods in discrete optimal control problems
The shape and smoothness of stable plasma configurations
The shooting approach in analyzing bang-bang extremals with simultaneous control switches
The shrinking projection method for solving variational inequality problems and fixed point problems in Banach spaces.
The Singular Set of an energy minimzing map from B4 to S2.