English

Convexity criteria and uniqueness of absolutely minimizing functions

Analysis of PDEs 2015-05-18 v1 Optimization and Control

Abstract

We show that absolutely minimizing functions relative to a convex Hamiltonian H:RnRH:\mathbb{R}^n \to \mathbb{R} are uniquely determined by their boundary values under minimal assumptions on H.H. Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in L.L^\infty.

Keywords

Cite

@article{arxiv.1003.3171,
  title  = {Convexity criteria and uniqueness of absolutely minimizing functions},
  author = {Scott N. Armstrong and Michael G. Crandall and Vesa Julin and Charles K. Smart},
  journal= {arXiv preprint arXiv:1003.3171},
  year   = {2015}
}

Comments

34 pages