scholarly journals Singular Abreu Equations and Minimizers of Convex Functionals with a Convexity Constraint

2019 ◽  
Vol 73 (10) ◽  
pp. 2248-2283 ◽  
Author(s):  
Nam Q. Le
Keyword(s):  
Convex Functionals ◽  
Convexity Constraint

scholarly journals On approximating minimizers of convex functionals with a convexity constraint by singular Abreu equations without uniform convexity

2020 ◽  
pp. 1-21
Author(s):  
Nam Q. Le
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Approximation Problem ◽  
Variational Problems ◽  
Uniform Convexity ◽  
Convex Functionals ◽  
Convexity Constraint ◽  
Fourth Order Equations ◽  
Appl Math

Abstract We revisit the problem of approximating minimizers of certain convex functionals subject to a convexity constraint by solutions of fourth order equations of Abreu type. This approximation problem was studied in previous articles of Carlier–Radice (Approximation of variational problems with a convexity constraint by PDEs of Abreu type. Calc. Var. Partial Differential Equations58 (2019), no. 5, Art. 170) and the author (Singular Abreu equations and minimizers of convex functionals with a convexity constraint, arXiv:1811.02355v3, Comm. Pure Appl. Math., to appear), under the uniform convexity of both the Lagrangian and constraint barrier. By introducing a new approximating scheme, we completely remove the uniform convexity of both the Lagrangian and constraint barrier. Our analysis is applicable to variational problems motivated by the original 2D Rochet–Choné model in the monopolist's problem in Economics, and variational problems arising in the analysis of wrinkling patterns in floating elastic shells in Elasticity.

scholarly journals Extensions of convex functionals on convex cones

1998 ◽  
Vol 25 (3) ◽  
pp. 381-386
Author(s):  
E. Ignaczak ◽  
A. Paszkiewicz
Keyword(s):  
Convex Cones ◽  
Convex Functionals

scholarly journals Some inequalities involving Heron and Heinz means of two convex functionals

2020 ◽  
Vol 46 (2) ◽  
pp. 345-365
Author(s):  
M. Raïssouli ◽  
S. Furuichi
Keyword(s):  
Convex Functionals
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