On approximation of convex functionals with a convexity constraint and general Lagrangians
arXiv:2504.07783
Abstract
In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order equations of Abreu type. Our result generalizes that of Le (Twisted Harnack inequality and approximation of variational problems with a convexity constraint by singular Abreu equations. Adv. Math. 434 (2023)) where the case of quadratically growing Lagrangians was treated.
Revised version, to appear in Proceedings of the Royal Society of Edinburgh. Section A. Mathematics