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arXiv · 2504.07783

On approximation of convex functionals with a convexity constraint and general Lagrangians

Young Ho Kim
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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.

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Young Ho Kim. 2025-04-10. On approximation of convex functionals with a convexity constraint and general Lagrangians. https://arxiv.org/abs/2504.07783

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