The principle of stationary action in the calculus of variations

Emanuel López; Alberto Molgado; José A. Vallejo

Communications in Mathematics (2012)

  • Volume: 20, Issue: 2, page 89-116
  • ISSN: 1804-1388

Abstract

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We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Our main intention in this regard is to expose precise mathematical conditions for critical paths to be minimum solutions in a variety of situations of interest in Physics. Our claim is that, with a few elementary techniques, a systematic analysis (including the domain for which critical points are genuine minima) of non-trivial models is possible. We present specific models arising in modern physical theories in order to make clear the ideas here exposed.

How to cite

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López, Emanuel, Molgado, Alberto, and Vallejo, José A.. "The principle of stationary action in the calculus of variations." Communications in Mathematics 20.2 (2012): 89-116. <http://eudml.org/doc/251396>.

@article{López2012,
abstract = {We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Our main intention in this regard is to expose precise mathematical conditions for critical paths to be minimum solutions in a variety of situations of interest in Physics. Our claim is that, with a few elementary techniques, a systematic analysis (including the domain for which critical points are genuine minima) of non-trivial models is possible. We present specific models arising in modern physical theories in order to make clear the ideas here exposed.},
author = {López, Emanuel, Molgado, Alberto, Vallejo, José A.},
journal = {Communications in Mathematics},
keywords = {stationary action; functional extrema; conjugate points; oscillatory solutions; Lane-Emden equations; stationary action; fundamental extrema; conjugate points; oscillatory solutions; Lane-Emden equations},
language = {eng},
number = {2},
pages = {89-116},
publisher = {University of Ostrava},
title = {The principle of stationary action in the calculus of variations},
url = {http://eudml.org/doc/251396},
volume = {20},
year = {2012},
}

TY - JOUR
AU - López, Emanuel
AU - Molgado, Alberto
AU - Vallejo, José A.
TI - The principle of stationary action in the calculus of variations
JO - Communications in Mathematics
PY - 2012
PB - University of Ostrava
VL - 20
IS - 2
SP - 89
EP - 116
AB - We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Our main intention in this regard is to expose precise mathematical conditions for critical paths to be minimum solutions in a variety of situations of interest in Physics. Our claim is that, with a few elementary techniques, a systematic analysis (including the domain for which critical points are genuine minima) of non-trivial models is possible. We present specific models arising in modern physical theories in order to make clear the ideas here exposed.
LA - eng
KW - stationary action; functional extrema; conjugate points; oscillatory solutions; Lane-Emden equations; stationary action; fundamental extrema; conjugate points; oscillatory solutions; Lane-Emden equations
UR - http://eudml.org/doc/251396
ER -

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