Giuseppe Rosario Mingione
"Sharp regularity results for functionals with non standard growth conditions"
Abstract: Integral functionals of the Calculus of Variations with non standard growth conditions are, roughly speaking, those whose energy densities cannot be controlled by a polynomial one and they are well defined in a space which is strictly smaller than the one in which they are coercive. As a consequence the associated Euler equations are non uniformly elliptic and exhibit funny type of degeneracies. Energy densities of this type arise from various situations and, in the last times, in the mathematical modeling of certain Non-Newtonian fluids. I will present some sharp regularity results for minimizers of such functionals (and for solutions to related equations) that reveals some phenomena that cannot be observed in the standard setting.
TUESDAY, March 19, 2002