On approximation of convex functionals with a convexity constraint and general Lagrangians
Analysis of PDEs
2025-10-14 v2
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.
Keywords
Cite
@article{arxiv.2504.07783,
title = {On approximation of convex functionals with a convexity constraint and general Lagrangians},
author = {Young Ho Kim},
journal= {arXiv preprint arXiv:2504.07783},
year = {2025}
}
Comments
Revised version, to appear in Proceedings of the Royal Society of Edinburgh. Section A. Mathematics