Antonia Passarelli di Napoli

Global Morrey regularity results for asymptotically convex variational problems

Abstract We prove some global, up to the boundary of a domain Ω ⊂ ℝ n , continuity and Morrey regularity results for almost minimizers of functionals of the form . The main assumptions are that g is asymptotically convex and that it has superlinear polynomial growth with respect its third argument. The integrand is only required to be locally bounded with respect to its third argument. Some discontinuous behavior with respect to its other arguments is also allowed. We also provide an application of our results to a class of variational problems with obstacles.

Higher differentiability of minimizers ofvariational integrals with Sobolev coefficients

In this paper we consider integral functionals of the form

Regularity of minimizers of autonomous convex variational integrals

We establish local higher integrability and differentiability results for minimizers of variational integrals

A \({C^{1,\alpha}}\) partial regularity result for non-autonomous convex integrals with discontinuous coefficients

\mathfrak{F}(v,\Omega) = \int_{\Omega} /! F(Dv(x)) \, dx

Regularity results for a priori bounded minimizers of non-autonomous functionals with discontinuous coefficients

over

Higher differentiability of solutions of parabolic systems with discontinuous coefficients

W^{1,p}

Regularity results for minimizers of integral functionals with nonstandard growth in Carnot–Carathéodory spaces

--Sobolev mappings

Higher differentiability of minimizers of convex variational integrals

u \colon \Omega \subset {\mathbb R}^n \to {\mathbb R}^N