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arXiv · 2312.11172

First variation of functional Wulff shapes

Jacopo Ulivelli
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Abstract

We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational lemma in the family of convex functions with compact domain. The resulting formula is then applied to evaluate the first variation of a class of functionals on convex functions. In particular, we extend a recent result by Huang, Liu, Xi, and Zhao.

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Jacopo Ulivelli. 2023-12-18. First variation of functional Wulff shapes. https://arxiv.org/abs/2312.11172

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