Calculus of Variations and Geometric Measure Theory

G. Buttazzo - M. S. Gelli - D. Lučić

Mass optimization problem with convex cost

created by lučić on 13 Apr 2022
modified by gelli on 11 Apr 2023


Published Paper

Inserted: 13 apr 2022
Last Updated: 11 apr 2023

Journal: SIAM J. Math. Anal.
Year: 2022

ArXiv: 2204.05416 PDF


In this paper we consider a mass optimization problem in the case of scalar state function, where instead of imposing a constraint on the total mass of the competitors, we penalize the classical compliance by a convex functional defined on the space of measures. We obtain a characterization of optimal solutions to the problem through a suitable PDE. This generalizes the case considered in the literature of a linear cost and applies to the optimization of a conductor where very low and very high conductivities have both a high cost, and then the study of nonlinear models becomes relevant.