A quest of regularity for problems with general growth

Mercoledi' 28 Settembre 2011 - Bianca Stroffolini


Mercoledi' 28 Settembre 2011, alle ore 12:15 in aula 2BC60, Bianca Stroffolini (Universita' di Napoli) terra' un seminario dal titolo "A quest of regularity for problems with general growth".

I will present some regularity results obtained with L. Diening and A. Verde for local minimizers of variational integrals with a general convex function. First of all, we generalized Uhlenbeck's result of (everywhere) Holder continuity of the gradient for radial functionals (depending on the modulus of the gradient) to the general case. We also present a unified approach to the superquadratic and subquadratic power case. Coming to a general vectorial case, partial regularity comes into the play, as shown in the famous counterexamples of Necas, and also Sverak & Yan. Partial regularity asserts the pointwise regularity of solutions/minimizers, in an open subset whose complement is negligible. We consider harmonic systems and prove a partial regularity result for the solution.

Rif. int. M. Bardi, C. Marchi, P. Mannucci

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