Legendre functions and the theory of characteristics
type: Dataset
description: We devise a framework encompassing the classical theory of characteristics and the theory valid in the convex case recently obtained by R.T. Rockafellar and P. Wolenski. It relies on a notion of transform introduced by I. Ekeland. It involves a class of functions called Ekeland functions which is large enough to encompass convex functions, concave functions and linear-quadratic functions, as well as the class of classical Legendre functions. We also introduce a class of functions called (generalized) Legendre functions which is not as large as the class of Ekeland functions but has better reciprocity properties. It is obtained by an extension procedure and it enables one to recover the usual Fenchel-Legendre transform of convex functions.
issued: 2026-06-03T03:00:52.606826
language: en
modified: 2026-06-03T03:00:52.606833
contact point: Organization
  fn: CCSD
keyword: characteristics
keyword: ekeland-function
keyword: ekeland-transform
keyword: hamilton-jacobi-equations
keyword: infoeu-reposemanticsreport
keyword: infoinfo-nacomputer-science-csnumerical-analysis-csna
keyword: legendre-function
keyword: legendre-transform
keyword: reports
keyword: subdifferential
landing page: https://hal.science/hal-00759367

Legendre functions and the theory of characteristics
type: Distribution
format: HTML
issued: 2026-06-03T03:00:52.745942
modified: 2026-06-03T03:00:52.566609
access URL: https://hal.science/hal-00759367

test_moissonnage_selune
type: Agent