Anna Verde

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.

A lower semi-continuity result for polyconvex functionals in SBV

We prove a semicontinuity theorem for an integral functional made up by a polyconvex energy and a surface term. Our result extends to the BV framework a well known result by John Ball.

Partial Regularity for Minimizers of Quasi-convex Functionals with General Growth

We prove a partial regularity result for local minimizers of quasiconvex variational integrals with general growth. The main tool is an improved A-harmonic approximation, which should be interesting also for classical growth.The convex hull property is the natural generalization of maximum principles from scalar to vector valued functions. Maximum principles for finite element approximations are often crucial for the preservation of qualitative properties of the respective physical model. In this work we develop a convex hull property for

Lower Semicontinuity in SBV for Integrals with Variable Growth

\mathbb{P }_1

On the Lipschitz character of orthotropic

conforming finite elements on simplicial non-obtuse meshes. The proof does not resort to linear structures of partial differential equations but directly addresses properties of the minimiser of a convex energy functional. Therefore, the result holds for very general nonlinear partial differential equations including e.g. the

harmonic functions

p