Ulivelli, J. (2025). First variation of functional Wulff shapes. Advances in Mathematics, 480(C), Article 110529. https://doi.org/10.1016/j.aim.2025.110529
Using an approximation procedure we establish, for suitable perturbations, a weighted 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 log-concave functions. In particular, we extend a recent result by Huang, Liu, Xi, and Zhao.
