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  • On approximating minimizers of convex functionals with a convexity constraint by singular Abreu equations without uniform convexity
Title: On approximating minimizers of convex functionals with a convexity constraint by singular Abreu equations without uniform convexity
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 Equations 58 (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.  more » « less
Award ID(s):
1764248
PAR ID:
10157537
Author(s) / Creator(s):
Date Published:
Journal Name:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
ISSN:
0308-2105
Page Range / eLocation ID:
1 to 21
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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