On central fields in the calculus of variations
Fabio Botelho
TL;DR
This paper establishes new sufficient conditions for local optimality in the calculus of variations by constructing stationary fields that preserve a generalized Hilbert integral, applicable to scalar and vector cases.
Contribution
It introduces a novel approach using stationary fields and a generalized Hilbert integral to determine local optimality in the calculus of variations.
Findings
Derived sufficient conditions for local optimality
Constructed stationary fields preserving the generalized Hilbert integral
Applicable to both scalar and vectorial calculus of variations
Abstract
This article develops sufficient conditions of local optimality for the scalar and vectorial cases of the calculus of variations. The results are established through the construction of stationary fields which keep invariant what we define as the generalized Hilbert integral.
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