Journal Article10.1007/BF01783466
One-dimensional non-coercive problems of the calculus of variations
TL;DR: In this paper, the existence of the minimum of the functional constraints in terms of a limitation on the slope of the slope was established. But the conditions for the minimum were not defined.
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Abstract: We establish a necessary and sufficient condition for the existence of the minimum of the functional\(\mathop \smallint \limits_a^b f(t,v'(t)\) dt in the class
in terms of a limitation on the slope d. We derive some applications regarding quasi-coercive and non-coercive integrands.
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Citations
On the Minimum Problem for a Class of Noncoercive Nonconvex Functionals
TL;DR: An existence result is given for the radially symmetric variational problem with nonconvex Lagrangians with respect to $
abla u$, which arise in different fields of mathematical physics such as optimal design and nonlinear elasticity.
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Another Theorem of Classical Solvability ‘In Small’ for One-Dimensional Variational Problems
TL;DR: In this article, a regularity theory is proposed for solving local minimizers of one-dimensional variational problems, which naturally complements the classical local theory and allows to resolve a number of problems which were previously unreachable.
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An Indirect Method of Nonconvex Variational Problems in Asplund Spaces: The Case for Saturated Measure Spaces
TL;DR: The purpose of this paper is to establish an existence result for nonconvex variational problems with Bochner integral constraints in separable Asplund spaces via the Euler--Lagrange inclusion, under the saturation hypothesis on measure spaces, which makes the Lyapunov convexity theorem valid in Banach spaces.
Necessary and Sufficient Conditions for Optimality of Nonconvex, NoncoerciveAutonomous Variational Problems with Constraints
Cristina Marcelli
- 01 Oct 2007
TL;DR: In this article, a necessary and sufficient condition for the optimality of a trajectory in the form of a DuBois-Reymond inclusion involving the subdifferential inequalities of Convex Analysis is presented.
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Bernard Dacorogna
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TL;DR: In this paper, the existence theorem for non-quasiconvex Integrands in the Scalar case has been established in the Vectorial case, where the objective function is to find the minimum of the minimum for a non-convex function.
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A general approach to the existence of minimizers of one-dimensional non-coercive integrals of the calculus of variations
TL;DR: In this article, a general approach to get the existence of minimizers for a class of one-dimensional nonparametric integrals of the calculus of variations with non-coercive integrands is presented.