Das Jacobische Kriterium der Variationsrechnung und die Oszillationseigenschaften linearer Differentialgleichungen 2. Ordnung. (Mit 1 Figur im Text) .
Decrease of C1,1 property in vector optimization
In the paper we generalize sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Rocca, and by authors with the help of the notion of ℓ-stability for vector functions.
Der Satz der Variationsrechnung, welcher dem Princip der kleinsten Wirkung in der Mechanik entspricht.
Derivatives of Hadamard type in scalar constrained optimization
Vsevolod I. Ivanov stated (Nonlinear Analysis 125 (2015), 270-289) the general second-order optimality condition for the constrained vector problem in terms of Hadamard derivatives. We will consider its special case for a scalar problem and show some corollaries for example for -stable at feasible point functions. Then we show the advantages of obtained results with respect to the previously obtained results.
Description du défaut de compacité de l'injection de Sobolev
Description of the lack of compactness for the Sobolev imbedding
We prove that any bounded sequence in a Hilbert homogeneous Sobolev space has a subsequence which can be decomposed as an almost-orthogonal sum of a sequence going strongly to zero in the corresponding Lebesgue space, and of a superposition of terms obtained from fixed profiles by applying sequences of translations and dilations. This decomposition contains in particular the various versions of the concentration-compactness principle.
Développements analytiques, pour servir à compléter la discussion de la variation seconde des intégrales définies multiples
Die hinreichenden Bedingungen des Extremums in der Theorie des Mayerschen Problems. (Mit 3 Figuren im Text)
Die Kriterien des Maximums und Minimums der einfachen Integrale in den isoperimetrischen Problemen. (Aus den Ber. der Kgl. Sächs. Ges. d. Wiss. Juli 1877)
Die Lagrangesche Multiplikatorenregel in der Variationsrechnung für den Fall von gemischten Bedingungen und die zugehörigen Grenzgleichungen bei variabeln Endpunkten.
Die Maxima und Minima der einfachen Integrale zwischen festen Grenzen
Differential inclusions with free time
Differential stability of solutions to air quality control problems in urban area
The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.
Dimension reduction for −Δ1
A 3D-2D dimension reduction for −Δ1 is obtained. A power law approximation from −Δp as p → 1 in terms of Γ-convergence, duality and asymptotics for least gradient functions has also been provided.
Direkte Herleitung von notwendigen Bedingungen der Variationsrechnung bei Mehrfachintegralen im Sinne von Carathéodory.
Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations
Discontinuous Hamiltonian flows for nonlinear control system.
Discrete twice optimal control systems
Distributed control for multistate modified Navier-Stokes equations
The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality conditions.
Doubles limites ordonnées et théorèmes de minimax
On introduit une variante des “doubles limites interchangeables” de Grothendieck, les “doubles limites ordonnées” et on en déduit un théorème de maximinimax. En introduisant des conditions de convexité convenables, on transforme celui-ci en un théorème de minimax. Ces résultats permettant de retrouver de façon simple un théorème de maximinimax de Simons.