Displaying similar documents to “Some Problems in the Calculus of Variations”

Nonsmooth Problems of Calculus of Variations via Codifferentiation

Maxim Dolgopolik (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper multidimensional nonsmooth, nonconvex problems of the calculus of variations with codifferentiable integrand are studied. Special classes of codifferentiable functions, that play an important role in the calculus of variations, are introduced and studied. The codifferentiability of the main functional of the calculus of variations is derived. Necessary conditions for the extremum of a codifferentiable function on a closed convex set and its applications to the nonsmooth...

Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies

Ken Shirakawa (2009)

Banach Center Publications

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In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of...

The fundamental theorem of algebra before Carl Friedrich Gauss.

Josep Pla i Carrera (1992)

Publicacions Matemàtiques

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This is a paper about the first attemps of demonstration of the fundamental theorem of algebra. Before, we analyze the tie between complex numbers and the number of roots of an equation of n-th degree. In the second paragraph, we see the relation between integration and the fundamental theorem. Finally, we observe the linear differential equation with constant coefficients and Euler's position about the fundamental theorem, and then we consider d'Alembert's,...