Lipschitz continuity for energy integrals with ellipticity conditions at infinity

Michela Eleuteri (Università di Modena e Reggio Emilia)

22/03/2017, ore 12, aula 2

In the general vector-valued case, we present some recent regularity results

obtained in cooperation with P. Marcellini and E. Mascolo. More precisely

we show the Lipschitz continuity of local minimizers to some integrals of

the Calculus of Variations where the Lagrangian has the form g(x, |Du|),

under some suitable p,q-growth conditions. We prove our results only for

large values of the gradient and without further structure conditions on the

integrand. We apply the regularity results to weak solutions to nonlinear

elliptic systems and to the case of some functionals with variable exponent.

We will open the seminar with a very general introduction concerning regularity

results for equations and systems in divergence form, in the framework of standard and nonstandard conditions.