TY - JOUR
T1 - Convexity Criteria and Uniqueness of Absolutely Minimizing Functions
AU - Armstrong, Scott N.
AU - Crandall, Michael G.
AU - Julin, Vesa
AU - Smart, Charles K.
N1 - Funding Information:
The third author was partially supported by the Academy of Finland, project #129784
PY - 2011/5
Y1 - 2011/5
N2 - We show that an absolutely minimizing function with respect to a convex Hamiltonian H:ℝn→ ℝis uniquely determined by its boundary values under minimal assumptions on 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∞.
AB - We show that an absolutely minimizing function with respect to a convex Hamiltonian H:ℝn→ ℝis uniquely determined by its boundary values under minimal assumptions on 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∞.
UR - http://www.scopus.com/inward/record.url?scp=79954590415&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79954590415&partnerID=8YFLogxK
U2 - 10.1007/s00205-010-0348-0
DO - 10.1007/s00205-010-0348-0
M3 - Article
AN - SCOPUS:79954590415
SN - 0003-9527
VL - 200
SP - 405
EP - 443
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -