English

Radial representation of lower semicontinuous envelope

Classical Analysis and ODEs 2013-09-18 v2

Abstract

We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper semicontinuity which plays the role of convexity, and allows to prove a radial representation result for nonconvex functions. An application to the relaxation of multiple integrals with constraints on the gradient is given.

Keywords

Cite

@article{arxiv.1211.6504,
  title  = {Radial representation of lower semicontinuous envelope},
  author = {Omar Anza Hafsa and Jean-Philippe Mandallena},
  journal= {arXiv preprint arXiv:1211.6504},
  year   = {2013}
}

Comments

16 pages

R2 v1 2026-06-21T22:45:14.045Z