[PDF] Top 20 Singular minimizers in the calculus of variations

... for the general case in Tonelli [1934]. We mention also Cesari [1983] as a good reference on this topic. The trick to proving existence results is to enlarge the space of admissible functions to a space with a topology ... See full document

... Abstract The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the ... See full document

... scale calculus theory can be applicable to any field in which dynamic processes are described by discrete- or continuous-time ...the calculus of variations and optimal control problems on time scales ... See full document

... The rule for the use of multiplicators was first published in 1788 by a French mathematician J. L. Lagrange in his Mécanique analytique for a wide class of tasks of the calculus of variations – so-called ... See full document

... Abstract. We apply the method of Hamilton shooting to obtain the well- posedness of boundary value problems for certain Hamiltonian systems and some estimates for their solutions. The examples of Hamiltonian functions ... See full document

... Parametric and nonparametric necessary and sufficient optimality conditions are established for a class of nonconvex variational problems with generalized fractional objective functions an[r] ... See full document

... Differential forms as invaluable tools have been available and applicable to various fields of study, see [–], while the systematic investigation of variational theory for differential forms has been less studied. Direct ... See full document

... The image enhancement or image recovery problems, which have recently re- ceived a considerable amount of attention, are an example of problems of cal- culus of variations that can be studied in the space of the ... See full document

... Congruence and Weak Bisimulation In order to extend ‘=’ to capture ∼L replace the two congruence rule by ‘=’ is preserved by all contexts.. for xF and ȳC summands of P and Q...[r] ... See full document

... 97 Therefore, given an admissible, piecewise differentiable section γ , a crucial question is establishing under what circumstances every admissible infinitesimal deformation vanishing a[r] ... See full document

... a heuristic argument of John [7] followed by the work of Post and Sivaloganathan [12] implies that F [·] admits at least countably many strong local minimizers in the space W id 1,p (Ω, R 2 ), which is a sharp ... See full document

... For a Bolza problem without any differential constraint, this condition is better known as the Legendre condition because, in 1786, Legendre obtained such a condition for the simplest pr[r] ... See full document

... Domingos Cavalcanti, Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term, Calculus of Variations and Partial Differential Equa[r] ... See full document

... [3] M. Bauderon, Differential geometry and Lagrangian formalism in the calculus of varia- tions, Differential Geometry, Calculus of Variations, and Their Applications, Lec- ture Notes in Pure and Appl. ... See full document

... After the Pontryagin's et al. (1962) book "Mathematical Theory of Optimal Processes", the Maximum Principle became the main tool of analysis in economics and management, physics, biology and so on. The absolute ... See full document

... of variations and many other ...classical calculus of variations, Mond and Hanson [4] formulated a con- strained variational problem as a mathematical pro- gramming problem and using Valentine’s [5] ... See full document

... This problem is formulated in the language of the calculus of variations or, more "commonly, as an optimal control problem: choose an extraction rate qt j.o to maximize the total discoun[r] ... See full document

... Lemma 1.. LANDAU, Einige Ungleichungen f¨ ur zweimal differentzierban funktionen, Proc. HARDY and J.E. LITTLEWOOD, Some integral inequalities connected with the calculus of variations, Q[r] ... See full document

... the calculus of variations (see 30] for an account on stochastic calculus of variation), is an extension of the Wiener integral and this justies our choice of using it as a stochastic integral with ... See full document

... The Lavrentiev gap phenomenon is a well-known effect in the calculus of variations, related to singularities of minimizers. In its presence, conforming finite element methods are incapable of ... See full document