Functional Analysis and Applications Seminar 

10/12/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building
Giuseppe Rosario Mingione, Universita degli Studi di Parma, Italy

Functionals with Non-Standard Growth, Lavrentev Phenomenon andRegularity

Functionals with non standard growth are coercive in a space which is strictly larger than the one where they are bounded and/or a priori finite. The regularity theory of minimizers differs from the usual one available for the standard functionals with polynomial growth, naturally defined in standard Sobolev spaces. I shall outline some regularity results and an approach to the regularity via Lavrentev phenomenon, suggested by a few constructions by Zhikov. Then, as a particular and enlightning case, I will describe the borderline situation of functionals with $p(x)$ growth, where a satisfying theory is available under certain optimal assumptions and I will suggest generalizations for functionals defined in more general spaces, today popular with the name of Orlicz-Musielak spaces.