4 papers
Optimizing bounds for energy-constrained optimal cooling problems in two dimensions
Pedro Blöss Braga, Giovanni Fantuzzi
We study optimal control problems for incompressible fluids in two-dimensional domains with a cold boundary and internal heat sources and sinks. Given a kinetic energy budget, meas…
Polyconvexity with Moments and Sums of Squares
Giovanni Fantuzzi, Didier Henrion, Martin Kru{ž}Ãk +2
A function of a matrix is polyconvex when it can be expressed as a convex function of the matrix minors. Polyconvexity is a regularity condition ensuring existence of minimizers in…
Internal heating profiles for which downward conduction is impossible
Ali Arslan, Giovanni Fantuzzi, John Craske +1
We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that $\l…
Sharpness and non-sharpness of occupation measure bounds for integral variational problems
Giovanni Fantuzzi, Ian Tobasco
We analyze two recently proposed methods to establish a priori lower bounds on the minimum of general integral variational problems. The methods, which involve either `occupation m…