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The Calculus of Variations is at the same time a classical subject, with long-standing open questions which have generated exciting discoveries in recent decades, and a modern subject in which new types of questions arise, driven by mathematical ...
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On the foundations of calculus of variations [PDF]
Transactions of the American Mathematical Society, 1941 The subject of this paper will be variational problems fF(x, t)dt = min in parameter form with fixed endpoints. The existence of rectifiable minimizing arcs has been proved under exceedingly general conditions. However, as soon as one wants to establish differentiability properties of the solutions one uses the Euler equations and must therefore assume
Busemann, Herbert, Mayer, Walther
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The variational calculus on time scales [PDF]
International Journal for Simulation and Multidisciplinary Design Optimization, 2010 The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the literature ...
Torrest Delfim F.M.
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Modeling of the Electronic Structure of Semiconductor Nanoparticles
Mathematics, 2023 This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations ...
Vasily B. Novozhilov +5 more
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Optimal Control Theory: Introduction to the Special Issue
Games, 2021 Optimal control theory is a modern extension of the classical calculus of variations [...]
Ellina Grigorieva
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, 2016 The Calculus of Variations is subject with a long and distinguished history, a great deal of diverse current activity, and close connections to other fields such as geometry and mathematical physics.
Živković, Josip
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The Approximation Solution of Some Calculus of Variation Problems Based Euler-Lagrange Equations [PDF]
Engineering and Technology Journal, 2016 The proposed method transforming some of calculus of variation problems into Euler-Lagrange equations, the simplicity and effectiveness of this illustrated through some ...
Zina Khalil Alabacy
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Fractal and Fractional, 2023 In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative.
Ricardo Almeida
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Problems of stability and well-posedness in the calculus of variations and related PDEs
, 2022 We present a collection of three closely related topics regarding the stability and well-posedness of minimization problems in the calculus of variations, namely the generic Tykhonov well-posedness with respect to linear perturbations, the generalized ...
Kalayanamit, Panas
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Exterior Convexity And Classical Calculus Of Variations [PDF]
, 2016 We study the relation between various notions of exterior convexity introduced in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009-1039.] with the classical notions of rank one convexity, quasiconvexity and polyconvexity.
Swarnendu Sil +3 more
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